$a_n$ and $b_n$ are sequences of arithmetic and geometric means, whose first three terms match. Given some...
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For $n>3$,
$a_{n}$ is arithmetic mean of $a_1$ through $a_{n-1}$
$b_{n}$ is geometric mean of $b_1$ through $b_{n-1}$
For $i=1,2,3$,
${{a}_{i}}$ = ${{b}_{i}}$
If $a_{1} = 3$, $a_{2017} = 7$, $a_{2018}=8$,
then
$$a_{2}^{2}+a_{3}^{2} = text{?}$$
What is the use of $b$ here? Where is it going to be used in solution?
sequences-and-series systems-of-equations
edited Nov 18 at 9:44
Blue
47k870148
asked Nov 18 at 9:25
Abhinov Singh
673
add a comment |
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For $n>3$,
$a_{n}$ is arithmetic mean of $a_1$ through $a_{n-1}$
$b_{n}$ is geometric mean of $b_1$ through $b_{n-1}$
For $i=1,2,3$,
${{a}_{i}}$ = ${{b}_{i}}$
If $a_{1} = 3$, $a_{2017} = 7$, $a_{2018}=8$,
then
$$a_{2}^{2}+a_{3}^{2} = text{?}$$
What is the use of $b$ here? Where is it going to be used in solution?
sequences-and-series systems-of-equations
edited Nov 18 at 9:44
Blue
47k870148
asked Nov 18 at 9:25
Abhinov Singh
673
1
many times i feel we at this site , are very quick to downvote a question. why cant it be possible that a person who is new getting accustomed to site is facjng problem. like i joined two months ago lot of my questions got downvoted. i think we can give newbies some time. question migjt be good
– maveric
Nov 18 at 9:29
See $2a_3=a_1+a_2$ and $b_3=sqrt{a_1a_2}$ .
– Yadati Kiran
Nov 18 at 9:34
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
For $n>3$,
$a_{n}$ is arithmetic mean of $a_1$ through $a_{n-1}$
$b_{n}$ is geometric mean of $b_1$ through $b_{n-1}$
For $i=1,2,3$,
${{a}_{i}}$ = ${{b}_{i}}$
If $a_{1} = 3$, $a_{2017} = 7$, $a_{2018}=8$,
then
$$a_{2}^{2}+a_{3}^{2} = text{?}$$
What is the use of $b$ here? Where is it going to be used in solution?
sequences-and-series systems-of-equations
edited Nov 18 at 9:44
Blue
47k870148
asked Nov 18 at 9:25
Abhinov Singh
673
For $n>3$,
$a_{n}$ is arithmetic mean of $a_1$ through $a_{n-1}$
$b_{n}$ is geometric mean of $b_1$ through $b_{n-1}$
For $i=1,2,3$,
${{a}_{i}}$ = ${{b}_{i}}$
If $a_{1} = 3$, $a_{2017} = 7$, $a_{2018}=8$,
then
$$a_{2}^{2}+a_{3}^{2} = text{?}$$
What is the use of $b$ here? Where is it going to be used in solution?
sequences-and-series systems-of-equations
sequences-and-series systems-of-equations
edited Nov 18 at 9:44
Blue
47k870148
asked Nov 18 at 9:25
Abhinov Singh
673
edited Nov 18 at 9:44
Blue
47k870148
asked Nov 18 at 9:25
Abhinov Singh
673
edited Nov 18 at 9:44
Blue
47k870148
edited Nov 18 at 9:44
Blue
47k870148
edited Nov 18 at 9:44
Blue
47k870148
47k870148
asked Nov 18 at 9:25
Abhinov Singh
673
asked Nov 18 at 9:25
Abhinov Singh
673
asked Nov 18 at 9:25
Abhinov Singh
673
673
1
many times i feel we at this site , are very quick to downvote a question. why cant it be possible that a person who is new getting accustomed to site is facjng problem. like i joined two months ago lot of my questions got downvoted. i think we can give newbies some time. question migjt be good
– maveric
Nov 18 at 9:29
See $2a_3=a_1+a_2$ and $b_3=sqrt{a_1a_2}$ .
– Yadati Kiran
Nov 18 at 9:34
add a comment |
1
many times i feel we at this site , are very quick to downvote a question. why cant it be possible that a person who is new getting accustomed to site is facjng problem. like i joined two months ago lot of my questions got downvoted. i think we can give newbies some time. question migjt be good
– maveric
Nov 18 at 9:29
See $2a_3=a_1+a_2$ and $b_3=sqrt{a_1a_2}$ .
– Yadati Kiran
Nov 18 at 9:34
1
1
many times i feel we at this site , are very quick to downvote a question. why cant it be possible that a person who is new getting accustomed to site is facjng problem. like i joined two months ago lot of my questions got downvoted. i think we can give newbies some time. question migjt be good
– maveric
Nov 18 at 9:29
many times i feel we at this site , are very quick to downvote a question. why cant it be possible that a person who is new getting accustomed to site is facjng problem. like i joined two months ago lot of my questions got downvoted. i think we can give newbies some time. question migjt be good
– maveric
Nov 18 at 9:29
See $2a_3=a_1+a_2$ and $b_3=sqrt{a_1a_2}$ .
– Yadati Kiran
Nov 18 at 9:34
See $2a_3=a_1+a_2$ and $b_3=sqrt{a_1a_2}$ .
– Yadati Kiran
Nov 18 at 9:34
add a comment |
1 Answer
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See $2a_3=a_1+a_2$, $a_2=a_1$ and $b_3=sqrt{a_1a_2}$. We get $a_2^2+a_3^2=18$.
answered Nov 18 at 9:36
Yadati Kiran
1,243417
add a comment |
1 Answer
1
active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
See $2a_3=a_1+a_2$, $a_2=a_1$ and $b_3=sqrt{a_1a_2}$. We get $a_2^2+a_3^2=18$.
answered Nov 18 at 9:36
Yadati Kiran
1,243417
add a comment |
up vote
0
down vote
See $2a_3=a_1+a_2$, $a_2=a_1$ and $b_3=sqrt{a_1a_2}$. We get $a_2^2+a_3^2=18$.
answered Nov 18 at 9:36
Yadati Kiran
1,243417
add a comment |
up vote
0
down vote
up vote
0
down vote
See $2a_3=a_1+a_2$, $a_2=a_1$ and $b_3=sqrt{a_1a_2}$. We get $a_2^2+a_3^2=18$.
answered Nov 18 at 9:36
Yadati Kiran
1,243417
See $2a_3=a_1+a_2$, $a_2=a_1$ and $b_3=sqrt{a_1a_2}$. We get $a_2^2+a_3^2=18$.
answered Nov 18 at 9:36
Yadati Kiran
1,243417
answered Nov 18 at 9:36
Yadati Kiran
1,243417
answered Nov 18 at 9:36
Yadati Kiran
1,243417
answered Nov 18 at 9:36
Yadati Kiran
1,243417
1,243417
add a comment |
add a comment |
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1
many times i feel we at this site , are very quick to downvote a question. why cant it be possible that a person who is new getting accustomed to site is facjng problem. like i joined two months ago lot of my questions got downvoted. i think we can give newbies some time. question migjt be good
– maveric
Nov 18 at 9:29
See $2a_3=a_1+a_2$ and $b_3=sqrt{a_1a_2}$ .
– Yadati Kiran
Nov 18 at 9:34