Let a1- a2- -a100 be an A-P- with a1 -3 and sp-i-1p ai- a- p- 100 for any integer n with 1- n - 20- let m-n- If sm-sn does not depend on n then a2 is

The correct option is D 9 s_m/s_n = s_5n/s_n = 5n/2[6+(5n 1)d]/n/2[6+(n 1)d] = 5[(6 d)+5nd]/[(6 d)+nd] d=6 or d=0If d=0 then a_2 =3 else ...

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Byju's Answer

Standard XII

Mathematics

Sum of n Terms

Let a1, a2, ...

Question

Let $a_{1}, a_{2}, . . . . . . . . . . . . . a_{100}$ be an A.P. with $a_{1} = 3$ and $s_{p} = p \sum i = 1 a i, a \leq p \leq 100$ for any integer n with $1 \leq n \leq 20$ , let $m = \sqrt{n}$ . If $\frac{s_{m}}{s_{n}}$ does not depend on n then $a_{2}$ is

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Solution

The correct option is D 9
$\frac{s_{m}}{s_{n}}$ = $\frac{s_{5 n}}{s_{n}}$ = $\frac{\frac{5 n}{2} [6 + (5 n - 1) d]}{\frac{n}{2} [6 + (n - 1) d]}$ = $\frac{5 [(6 - d) + 5 n d]}{[(6 - d) + n d]}$
d=6 or d=0
If d=0 then $a_{2}$ =3 else $a_{2}$ = 9
For single choice, more appropriate choice is 9
$∴ a_{2} = 3 + 6 = 9$

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Leta1,a2,.............a100 be an A.P. with a1=3 and sp=p∑i=1ai,a≤p≤100 for any integer n with 1≤n≤20, let m=√n. If smsn does not depend on n then a2 is

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Let $a_{1}, a_{2}, . . . . . . . . . . . . . a_{100}$ be an A.P. with $a_{1} = 3$ and $s_{p} = p \sum i = 1 a i, a \leq p \leq 100$ for any integer n with $1 \leq n \leq 20$ , let $m = \sqrt{n}$ . If $\frac{s_{m}}{s_{n}}$ does not depend on n then $a_{2}$ is