Question

Find the sum:

1 + (2) + (5) + (8) + ... + (236)

Answer 1

Clearly the terms of the series $2+5+8+...+236$ form an AP with first term $a=2$ and common difference $d=3$.Let there be $n$ terms in given series $2+5+8+...+236$. Then
$a_n=236\Rightarrow a+(n-1)d=236$
$\Rightarrow 2+(n-1)\times 3=236$
$\Rightarrow (n-1)\times 3=234$
$\Rightarrow n-1=78$
$\Rightarrow n=79$
therefore sum of series $2+5+8+...+236=\frac{n}{2}(a+l)=\frac{79}{2}(2+236)=79\times 119=9401$