Question

In A.P. the first term is -4, the last term is 29 and the sum of all its terms is 150. Find its common difference.

Answer 1

Given in a AP $a=$ first term $=-4$

$l=$ last term $=29$

the sum of all terms $=150$

Let's' be a common difference of AP

$l=a+(n-1)d$ ______ (1)

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

$\Rightarrow S=\frac{n}{2}[a+l]$

$\Rightarrow 150=\frac{n}{2}[-4+29]=\frac{25n}{2}$

$[n=12]$ now from equation (1)

$29=-4+11d$

$33=11d$

$d=3$

Hence a common difference is 3