Question

If the sum of $7$ terms of an A.P is $49$ and that of $17$ terms is $289$, find the sum of $n$ terms.

• A. $n^{}$
• B. $n^2$
• C. $n^3$
• D. $n^4$

Answer 1

The correct option is B $n^2$

Formula:

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

Given,

$S_7=\frac{7}{2}[2a+(7-1\left)d\right]=49$

solving the above equation, we get,

$\frac{14-6d}{2}=a$

$\Rightarrow a=7-3d$..........(1)

$S_{17}=\frac{17}{2}[2a+(17-1\left)d\right]=289$

solving the above equation, we get,

$\frac{34-16d}{2}=a$

$\Rightarrow a=17-8d$..........(2)

equating (1) and (2), we get

$d=2$

using the value of "d", we get,

$a=1$

we have,

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$=\frac{n}{2}\left[2\right(1)+(n-1\left)\right(2\left)\right]$

$=\frac{n}{2}\left(2n\right)$

$\therefore S_n=n^2$