Question

The sum of first $7$ terms of an A.P. is $49$ and that of first $17$ terms of it is $289$. Find the sum of first n terms.

Answer 1

Sum of first $7$ terms $=49$

$\Rightarrow$$\frac{7}{2}(2a+6d)=49$

$\Rightarrow$$a+3d=7$

$\Rightarrow$Sum of first $17$ terms $=289$

$\Rightarrow$$\frac{17}{2}(2a+16d)=289$

$\Rightarrow$$a+8d=17$

$\Rightarrow$$(a+8d)-(a+3d)=17-7$

$\Rightarrow$$5d=10$

$\Rightarrow$$d=2$

$\Rightarrow$$a=1$

Sum of first $n$ terms

$=\frac{n}{2}(2+2n-2)$
$=n^2$