Question

In an ap the sum of first n term is 3 x square by 2 + 13 x by 2 find the 25th terms

Answer 1

Solution :

$\sf\: S_{n} \: = \dfrac{3 {x}^{2} + 13x }{2}$

$\sf\: a_{n} \: = S_{n} - S_{n - 1}$

$\sf \: a_{25} \: = S_{25} - S_{24}$

$\sf \rightarrow \: \dfrac{3( {25)}^{2} + 13(25)}{2} - \dfrac{3 ({24)}^{2} + 13(24)}{2}$

$\sf \rightarrow \dfrac{1}{2} \times 3( {25)}^{2} - {24}^{2} ) + 13(25 - 24)$

$\sf \rightarrow \dfrac{1}{2} \times (3 \times 49 + 13)$

$\sf \rightarrow \dfrac{1}{2} \times (147 + 13)$

$\sf \rightarrow \dfrac{1}{2} \times 160$

$\red{\sf \rightarrow \: 80}$

$\therefore$ 25th term is 80