Question

The number of terms of the $AP3,7,11,15\dots$ to be taken so that the sum is $210$, is :

• A. 10
• B. 12
• C. -1
• D. 2

Answer 1

Answer: (A)

Given series is $3,7,11,15,...$
whose first term is $3$ ,
common difference $4$ and sum is $210$ .
Let n be the number of term.
$\therefore$ $S=\frac{n}{2}[2a+(n-1)d]$
$\Rightarrow$ $210=\frac{n}{2}[6+(n-1)4]$
$\Rightarrow$ $210=n[3+2n-2]$
$\Rightarrow$ $2n^2+n-210=0$
$\Rightarrow$ $n=10$