Question

Solve
The first term of an $A.P.$ is $1$ and the sum of first $15$ terms is $225$, find the common difference.

Answer 1

Given $a=1$

$S_{15}=225S_{15}=\frac{15}{2}[2a+(15-1\left)d\right]\Rightarrow 225=\frac{15}{2}[2\times 1+14d]\Rightarrow \frac{225\times 2}{15}=2+14d\Rightarrow 30=2+14d\Rightarrow 14d=28\Rightarrow d=2$