Question

If sum of $n$ terms is $\frac{3n^2}{2}-\frac{13n}{2}$ find the ${25}^{th}$ term.

Answer 1

$S_n=\frac{3n^2}{2}-\frac{13n}{2}\left(\text{Given}\right)$

Now,

$S_{24}=\frac{3\cdot {\left(24\right)}^2}{2}-\frac{13\times 24}{2}=864-156=708$

$S_{25}=\frac{3\cdot {\left(25\right)}^2}{2}-\frac{13\times 25}{2}=\frac{1875-325}{2}=775$

Therefore,

$T_{25}=S_{25}-S_{24}=775-708=67$

Hence the ${25}^{th}$ term of the given series will be $67$.