Question

Find the sum of the first $24$ terms of an AP whose $n^{\text{th}}$ term is given by $t_n=3+2n.$

• A. 568
• B. 624
• C. 564
• D. 672

Answer 1

The correct option is D

672

Given, $t_n=3+2n.$

$\therefore t_1=3+2\times 1=5$

$t_2=3+2\times 2=7$

$t_3=3+2\times 3=9$

Note that $t_2-t_1=t_3-t_2=2.$

Thus, the common difference of the AP is 2.

Therefore, the AP is 5, 7, 9, 11 . . .

The sum to $n$ terms of an AP with first term $a$ and common difference $d$ is

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

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

$=12(10+46)=672$