Question

The number of terms of the series $5,7,9,...$ that must be taken in order to have sum of $1020$ is

• A. $20$
• B. $30$
• C. $40$
• D. $50$

Answer 1

Answer: (B)

$30$

Sum of $n$ terms of the given AP $=1020$, with first term as $5$ and common difference as $2$.

Sum of n terms of an A.P. $=\frac{n}{2}[2\times a_0+(n-1)\times d]$
According to the sum formula for $n$ terms of an A.P, we get

$1020=\frac{n}{2}(2\times 5+(n-1\left)2\right)$
$1020=n(n+4)$
$n^2+4n-1020=0$
Solving for $n$, we get
$n=30$

Hence, option B.