Question

If $a_1,a_2,a_3,\cdots$ are in A.P. such that $a_1+a_7+a_{16}=40$, then the sum of the first $15$ terms of this A.P. is :

• A. $150$
• B. $120$
• C. $280$
• D. $200$

Answer 1

The correct option is D $200$

$a_1,a_2,a_3,\cdots ,a_n$ are in A.P.
$a_1+a_7+a_{16}=40\Rightarrow a+a+6d+a+15d=40\Rightarrow 3a+21d=40\Rightarrow a+7d=\frac{40}{3}\Rightarrow S_{15}=\frac{15}{2}[2a+14d]\Rightarrow S_{15}=15[a+7d]\therefore S_{15}=200$