Question

The sum of the first 20 terms of an AP is known to be 1280, and the common difference is 20. Then, the fourth term of the AP will be __.

• A. -64
• B. -66
• C. -62
• D. -60

Answer 1

The correct option is B -66

Given that the sum of the first 20 terms of the AP, $S_{20}$ is 1280.
Let the first term and the common difference of the AP be $a$ and $d$ respectively.
From question, $d=20.$
The sum to $n$ terms of the AP is given by
$S_n=\frac{n}{2}(2a+(n-1\left)d\right).$
$\therefore S_{20}=\frac{20}{2}(2a+(20-1\left)20\right)=1280$
$\Rightarrow 2a+19\left(20\right)=128$
$\Rightarrow a=-126$

We know that the $n^{\text{th}}$ term of the AP is given by
$a_n=a+(n-1)d.$
$\therefore a_4=a+(4-1)d$
$=-126+(3\times 20)$
$=-66$
Thus, the $4^{\text{th}}$ term of the AP is -66.