Question

The sum of the first 20 terms of an AP is 1280, the common difference is 20. Then the fourth term of the AP is .

• A. -64
• B. -66
• C. -62
• D. -60

Answer 1

The correct option is B -66

Given, the sum of first 20 terms is 1280.
Let the first term be $a$, and the common difference be $d$
$d$ = 20 (given)
$\Rightarrow S_{20}=\frac{20}{2}(2a+(20-1\left)20\right)=1280$
$\Rightarrow 10(2a+19(20\left)\right)=1280$
Now, from the above equation we can calculate the value of $a$,
$a=-126$

Fourth term = $a_4$
$a_4=a+(4-1)d$
$=-126+(4-1)20$
$=-126+60=-66$