Question

Find the sum of the following arithmetic series: $2+9+16+23+30+......to20$terms.

• A. $1310$
• B. $1340$
• C. $1370$
• D. $1350$

Answer 1

Answer: (C)

$1370$

Now, Second term - First term = 9 - 2 = 7
Third term - Second term = 16 - 9 = 7
Fourth term - Third term = 23 - 16 = 7
Therefore, common difference of the given arithmetic series is 7.
The number of terms of the given A.P. series (n) = 20
d = 7
$S=\frac{n}{2}[2a+(n-1\left)d\right]$
Therefore, the required sum of first 20 terms of the series,
$S=\frac{20}{2}[2\times 2+(20-1\left)7\right]$
$S=\frac{20}{2}[4+133]$
$S=10\left[137\right]$
$S=1370$