Question

Sum of first 20 terms of an AP is and its first term is 7. Find its ${24}^{th}$ term.

Answer 1

First term of the A.P (a) = 7; sum of first 20 terms =
The sum of first in terms of an AP, $Sn=\frac{n}{2}[2a+(n-1\left)d\right]$,
Where a is the first term and d is the common difference.$\therefore S_{20}=\frac{20}{2}[2\times 7+(20-1\left)d\right]=-240$
$\Rightarrow 10[14+19d]=-240\Rightarrow 14+19d=-24\Rightarrow 19d=-24-14\Rightarrow 19d=-38\Rightarrow d=-2$
now, ${24}^{th}$ term of the AP, $a_{24}=a+(24-1)d$
on putting respective values of a and d, we get
$a_{24}+7+23\times (-2)=7-46=-39$
hence, ${24}^{th}$ term of the given AP is -39.