Question

Find the sum of first $24$ terms of the list of numbers whose $n^{th}$ term is given by $a_n=3+2n$.

• A. 568
• B. 624
• C. 564
• D. 672

Answer 1

The correct option is D

672

As $a_n=3+2n$,

$a_1=3+2\times 1=5$

$a_2=3+2\times 2=7$

$a_3=3+2\times 3=9$

List of numbers becomes 5, 7, 9, 11 . . .

Here, $7–5=9–7=11–9=2$ and so on.

Hence, it forms an AP with common difference $d=2$.

To find $S_{24}$,

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
we have $n=24,a=5,d=2$.

$\therefore S_{24}=\frac{24}{2}\left(2\right(5)+(24-1\left)2\right)$

$=12(10+46)=672$