Question

Sum of the first $20$ terms of an AP is $-240,$ and its first term is $7.$ Find its $24$th term.

• A. $-24$
• B. $-39$
• C. $1$
• D. $0$

Answer 1

Answer: (B)

$-39$

Given : Sum of $20$ terms of an AP $=-240$ and First term $7$

Sum of first $n$ terms of an AP is given as

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

$n=20,S=-240,a=7$

$\Rightarrow -240=\frac{20}{2}[2\times 7+(20-1\left)d\right]$

$\Rightarrow -240=10[14+19d]$

$\Rightarrow -240=140+190d$

$\Rightarrow -190d=140+240$

$\Rightarrow -190d=380$

$\Rightarrow d=\frac{380}{-190}=-2$

$n^{th}$ term of an AP $=a_n=a+(n-1)d$

$\Rightarrow a_{24}=7+(24-1)(-2)$

$\Rightarrow a_{24}=7-46$

$\Rightarrow a_{24}=-39$