Question

Lets, $s_1\left(n\right)$ be the sum of the first n terms of the arithmetic progression 8, 12, 16,... and let $s_2\left(n\right)$ 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

Answer: (B)

$260$

AP: $8,12,16,....$

$a=8,d=4$

$S_n=\frac{n}{2}[16+(n-1\left)4\right]=n(2n+6)$

AP: $17,19,21,...$

$a=17,d=2$

$S_n=\frac{n}{2}[34+(n-1\left)2\right]=n(n+16)$

$n(2n+6)=n(n+16)2n^2+6n=n^2+16n{n}^2-10n=0n=10$

$S_n=n(2n+6)=10\left(26\right)=260$