Question

In an AP the first term is 8, nth term is 33 and the sum to n terms is 123. Find the number of terms and common difference.

Answer 1

Given,

$a=8,a_n=33,S_n=123$

$a_n=a+(n-1)d$

$\Rightarrow 33=8+(n-1)d$

$\Rightarrow (n-1)d=25$

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

$123=\frac{n}{2}[2\times 8+25]$

$246=n[16+25]$

$\Rightarrow n=\frac{246}{41}$

$\therefore n=6$

$(n-1)d=25$

$(6-1)d=25$

$\therefore d=5$