Question

If a${}_1,a_2,a_3$ ,..... 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. 200
• B. 280
• C. 120
• D. 150

Answer 1

Answer: (A)

$a_1+a_7+a_{16}=40$
$a+a+6d+a+15d=40$
$\Rightarrow 3a+21d=40\Rightarrow a+7d=\frac{40}{3}$
$S_{15}=\frac{15}{2}(2a+14d)=15(a+7d)$
$S_{15}=15\times \frac{40}{3}\Rightarrow 200S_{15}=200$