Question

Calculate the sum of the following arithmetic series: $1+5+9+13+17+......to30$ terms.

• A. $1500$
• B. $1700$
• C. $1550$
• D. $1770$

Answer 1

Answer: (D)

$1770$

The common difference of the given arithmetic series is 4.
The number of terms of the given A.P. series (n) = 30
$S=\frac{n}{2}[2a+(n-1\left)d\right]$
Therefore, the required sum of first 30 terms of the series,
$S=\frac{30}{2}[2\times 1+(30-1\left)4\right]$
$S=\frac{30}{2}[2+116]$
$S=15\left[118\right]$
$S=1770$