Question

Let $s_1$ (n) be the sum of the first n terms of the arithmetic progression 8, 12, 16,..... and let $s_2$ (n) be the sum of the first n terms of arithmetic progression 17, 19,21 ..... If for some value of n, $s_1\left(n\right)=s_2\left(n\right)$ then this common sum is

• A. not uniquely determinable
• B. 260
• C. 216
• D. 200

Answer 1

The correct option is B 260

$s_1\left(n\right)=\frac{n}{2}[2.8+(n-1\left)4\right]$ $s_2\left(n\right)=\frac{n}{2}[2.17+(n-1\left)2\right]$
$s_1\left(n\right)=s_2\left(n\right)$
$\frac{n}{2}[2.8+(n-1\left)4\right]=\frac{n}{2}[2.17+(n-1\left)2\right]$
$2(n-1)=18$
$n-1=9$
$n=10$
$s_1\left(10\right)=5[16+36]=260=s_2\left(10\right)$