1025th term of the given sequence.Finding the nth term in a repeating number sequenceHow to show all the terms in a sequence are greater than a number?Find first term and common difference of Arithmetic Sequence, given two other termsThe second term of an arithmetic sequence is $13$ and $5^th$ term is $31$. What is the $17^th$ term of the sequence?Unique sequenceHow to calculate the nth term of sequence that increases by n?Finding arithmetic sequence first termGeometric Sequence with formula for kth term.Description of an Increasing Maximum Value in a Sequence of IntegersWhat is the general term of this sequence of integers?
What would be the effects of (relatively) widespread precognition on the stock market?
What does Windows' "Tuning up Application Start" do?
Install suspension forks on non-suspension bike
How does the Gameboy's memory bank switching work?
Remove side menu(right side) from finder
Router restarts after big git push or big file upload
How can I create an article with a title like the 1960s Journal of Finance?
Is there an English word to describe when a sound "protrudes"?
Soft constraints and hard constraints
Why didn't Balak request Bilam to bless his own people?
What is this light passenger prop airplane which crash landed in East Kalimantan, Borneo in 1983?
Can a creature sustain itself by eating its own severed body parts?
Improving an O(N^2) function (all entities iterating over all other entities)
How can electronics on board JWST survive the low operating temperature while it's difficult to survive lunar nights?
Linux ext4 restore file and directory access rights after bad backup/restore
I want light controlled by one switch, not two
Ethiopian Airlines tickets seem to always have the same price regardless of the proximity of the date?
What is the intuition for higher homotopy groups not vanishing?
Difference between string += s1 and string = string + s1
Making an example from 'Clean Code' more functional
Does a hash function have a Upper bound on input length?
How can I show that the speed of light in vacuum is the same in all reference frames?
Raspbian gcc does not know '.intel_syntax'?
Brute-force the switchboard
1025th term of the given sequence.
Finding the nth term in a repeating number sequenceHow to show all the terms in a sequence are greater than a number?Find first term and common difference of Arithmetic Sequence, given two other termsThe second term of an arithmetic sequence is $13$ and $5^th$ term is $31$. What is the $17^th$ term of the sequence?Unique sequenceHow to calculate the nth term of sequence that increases by n?Finding arithmetic sequence first termGeometric Sequence with formula for kth term.Description of an Increasing Maximum Value in a Sequence of IntegersWhat is the general term of this sequence of integers?
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
Consider the following sequence - $$ 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8, ... $$
In this sequence, what will be the $ 1025^th, term $
So, when we write down the sequence and then write the value of $ n $ (Here, $n$ stands for the number of the below term) above it We can observe the following -
1 - 1
2 - 2
3 - 2
4 - 4
5 - 4
. . .
8 - 8
9 - 8
. . .
We can notice that $ 4^th$ term is 4 and similarly, the $ 8^th$ term is 8.
So the $ 1025^th$ term must be 1024 as $ 1024^th $ term starts with 1024.
So the value of $ 1025^th$ term is $ 2^10 $ .
Is there any other method to solve this question?
sequences-and-series
asked 8 hours ago
KaushikKaushik
716 bronze badges
$endgroup$
add a comment |
$begingroup$
Consider the following sequence - $$ 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8, ... $$
In this sequence, what will be the $ 1025^th, term $
So, when we write down the sequence and then write the value of $ n $ (Here, $n$ stands for the number of the below term) above it We can observe the following -
1 - 1
2 - 2
3 - 2
4 - 4
5 - 4
. . .
8 - 8
9 - 8
. . .
We can notice that $ 4^th$ term is 4 and similarly, the $ 8^th$ term is 8.
So the $ 1025^th$ term must be 1024 as $ 1024^th $ term starts with 1024.
So the value of $ 1025^th$ term is $ 2^10 $ .
Is there any other method to solve this question?
sequences-and-series
asked 8 hours ago
KaushikKaushik
716 bronze badges
$endgroup$
1
$begingroup$
This method is very efficient. Why would you want another ?
$endgroup$
– Yves Daoust
7 hours ago
add a comment |
$begingroup$
Consider the following sequence - $$ 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8, ... $$
In this sequence, what will be the $ 1025^th, term $
So, when we write down the sequence and then write the value of $ n $ (Here, $n$ stands for the number of the below term) above it We can observe the following -
1 - 1
2 - 2
3 - 2
4 - 4
5 - 4
. . .
8 - 8
9 - 8
. . .
We can notice that $ 4^th$ term is 4 and similarly, the $ 8^th$ term is 8.
So the $ 1025^th$ term must be 1024 as $ 1024^th $ term starts with 1024.
So the value of $ 1025^th$ term is $ 2^10 $ .
Is there any other method to solve this question?
sequences-and-series
asked 8 hours ago
KaushikKaushik
716 bronze badges
$endgroup$
Consider the following sequence - $$ 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8, ... $$
In this sequence, what will be the $ 1025^th, term $
So, when we write down the sequence and then write the value of $ n $ (Here, $n$ stands for the number of the below term) above it We can observe the following -
1 - 1
2 - 2
3 - 2
4 - 4
5 - 4
. . .
8 - 8
9 - 8
. . .
We can notice that $ 4^th$ term is 4 and similarly, the $ 8^th$ term is 8.
So the $ 1025^th$ term must be 1024 as $ 1024^th $ term starts with 1024.
So the value of $ 1025^th$ term is $ 2^10 $ .
Is there any other method to solve this question?
sequences-and-series
sequences-and-series
asked 8 hours ago
KaushikKaushik
716 bronze badges
asked 8 hours ago
KaushikKaushik
716 bronze badges
asked 8 hours ago
KaushikKaushik
716 bronze badges
asked 8 hours ago
KaushikKaushik
716 bronze badges
asked 8 hours ago
KaushikKaushik
716 bronze badges
716 bronze badges
1
$begingroup$
This method is very efficient. Why would you want another ?
$endgroup$
– Yves Daoust
7 hours ago
add a comment |
1
$begingroup$
This method is very efficient. Why would you want another ?
$endgroup$
– Yves Daoust
7 hours ago
1
1
$begingroup$
This method is very efficient. Why would you want another ?
$endgroup$
– Yves Daoust
7 hours ago
$begingroup$
This method is very efficient. Why would you want another ?
$endgroup$
– Yves Daoust
7 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
A higher brow way of writing the same thing is to say the $n^th$ term is
$2^lfloor log_2 nrfloor$, then to evaluate that at $n=1025$. The base $2$ log of $1025$ is slightly greater than $10$, so the term is $2^10=1024$.
answered 8 hours ago
Ross MillikanRoss Millikan
309k24 gold badges203 silver badges381 bronze badges
$endgroup$
add a comment |
$begingroup$
In binary, the term indexes
$$1,10,11,100,101,110,111,1000,1001,1010,1011,1100,1101,1110,1111,cdots$$
become
$$1,10,10,100,100,100,100,1000,1000,1000,1000,1000,1000,1000,1000,cdots$$
So for any term, clear all bits but the most significant.
$$10000000001to10000000000.$$
answered 7 hours ago
Yves DaoustYves Daoust
142k9 gold badges85 silver badges241 bronze badges
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3299825%2f1025th-term-of-the-given-sequence%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
A higher brow way of writing the same thing is to say the $n^th$ term is
$2^lfloor log_2 nrfloor$, then to evaluate that at $n=1025$. The base $2$ log of $1025$ is slightly greater than $10$, so the term is $2^10=1024$.
answered 8 hours ago
Ross MillikanRoss Millikan
309k24 gold badges203 silver badges381 bronze badges
$endgroup$
add a comment |
$begingroup$
A higher brow way of writing the same thing is to say the $n^th$ term is
$2^lfloor log_2 nrfloor$, then to evaluate that at $n=1025$. The base $2$ log of $1025$ is slightly greater than $10$, so the term is $2^10=1024$.
answered 8 hours ago
Ross MillikanRoss Millikan
309k24 gold badges203 silver badges381 bronze badges
$endgroup$
add a comment |
$begingroup$
A higher brow way of writing the same thing is to say the $n^th$ term is
$2^lfloor log_2 nrfloor$, then to evaluate that at $n=1025$. The base $2$ log of $1025$ is slightly greater than $10$, so the term is $2^10=1024$.
answered 8 hours ago
Ross MillikanRoss Millikan
309k24 gold badges203 silver badges381 bronze badges
$endgroup$
A higher brow way of writing the same thing is to say the $n^th$ term is
$2^lfloor log_2 nrfloor$, then to evaluate that at $n=1025$. The base $2$ log of $1025$ is slightly greater than $10$, so the term is $2^10=1024$.
answered 8 hours ago
Ross MillikanRoss Millikan
309k24 gold badges203 silver badges381 bronze badges
answered 8 hours ago
Ross MillikanRoss Millikan
309k24 gold badges203 silver badges381 bronze badges
answered 8 hours ago
Ross MillikanRoss Millikan
309k24 gold badges203 silver badges381 bronze badges
answered 8 hours ago
Ross MillikanRoss Millikan
309k24 gold badges203 silver badges381 bronze badges
309k24 gold badges203 silver badges381 bronze badges
add a comment |
add a comment |
$begingroup$
In binary, the term indexes
$$1,10,11,100,101,110,111,1000,1001,1010,1011,1100,1101,1110,1111,cdots$$
become
$$1,10,10,100,100,100,100,1000,1000,1000,1000,1000,1000,1000,1000,cdots$$
So for any term, clear all bits but the most significant.
$$10000000001to10000000000.$$
answered 7 hours ago
Yves DaoustYves Daoust
142k9 gold badges85 silver badges241 bronze badges
$endgroup$
add a comment |
$begingroup$
In binary, the term indexes
$$1,10,11,100,101,110,111,1000,1001,1010,1011,1100,1101,1110,1111,cdots$$
become
$$1,10,10,100,100,100,100,1000,1000,1000,1000,1000,1000,1000,1000,cdots$$
So for any term, clear all bits but the most significant.
$$10000000001to10000000000.$$
answered 7 hours ago
Yves DaoustYves Daoust
142k9 gold badges85 silver badges241 bronze badges
$endgroup$
add a comment |
$begingroup$
In binary, the term indexes
$$1,10,11,100,101,110,111,1000,1001,1010,1011,1100,1101,1110,1111,cdots$$
become
$$1,10,10,100,100,100,100,1000,1000,1000,1000,1000,1000,1000,1000,cdots$$
So for any term, clear all bits but the most significant.
$$10000000001to10000000000.$$
answered 7 hours ago
Yves DaoustYves Daoust
142k9 gold badges85 silver badges241 bronze badges
$endgroup$
In binary, the term indexes
$$1,10,11,100,101,110,111,1000,1001,1010,1011,1100,1101,1110,1111,cdots$$
become
$$1,10,10,100,100,100,100,1000,1000,1000,1000,1000,1000,1000,1000,cdots$$
So for any term, clear all bits but the most significant.
$$10000000001to10000000000.$$
answered 7 hours ago
Yves DaoustYves Daoust
142k9 gold badges85 silver badges241 bronze badges
edited 7 hours ago
answered 7 hours ago
Yves DaoustYves Daoust
142k9 gold badges85 silver badges241 bronze badges
answered 7 hours ago
Yves DaoustYves Daoust
142k9 gold badges85 silver badges241 bronze badges
answered 7 hours ago
Yves DaoustYves Daoust
142k9 gold badges85 silver badges241 bronze badges
142k9 gold badges85 silver badges241 bronze badges
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3299825%2f1025th-term-of-the-given-sequence%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
This method is very efficient. Why would you want another ?
$endgroup$
– Yves Daoust
7 hours ago