Question

Calculate the sum of the ${15}^{th}$ to ${25}^{th}$ terms (inclusive) of the arithmetic sequence $3,8,13,18,...$

• A. $1001$
• B. $1003$
• C. $1005$
• D. $1007$

Answer 1

Answer: (C)

$1005$

first term $a=3d=5$
We know the formula,
$S_n=\frac{n}{2}[2\times a+(n-1\left)d\right]$
$S_{15}=\frac{15}{2}[2\times 3+(15-1\left)5\right]$
$S_{15}=570$
$S_{25}=\frac{25}{2}[2\times 3+(25-1\left)5\right]$
$S_{25}=1575$
Therefore the sum of the ${15}^{th}$ to ${25}^{th}$ terms$=1575-570=1005$