Question

The sum of the first n term of an AP is given by Sn=n/2[3n+13], then find its 25th term

Answer 1

$Hiii$‼

Given, sum of n terms
$s_{n} = \frac{n}{2} (3n + 13)$

$s_{1} = \frac{1}{2} (3 \times 1 + 13)$
$=> \frac{1}{2} \times 16$
$=> 8$

$s_{2} = \frac{2}{2} (3 \times 2 + 13)$
$=> 6 + 13$
$=> 19$

So, first term $a_{1} = 8$
Second term $a_{2} = 19 - 8 = 3$

Common difference $d = a_{2} - a_{1}$
$= > 11 - 8$
$= > 3$

As we know,
$a_{n} = a + (n - 1)d$

$a_{25} = 8 + (25 - 1)3$
$=> 8 + (24)3$
$=> 8 + 72$
$=> 80$

Therefore, the 25th term is 80.