Question

Find the sum of the following arithmetic progression:

$2,5,8,11,.......,59$.

Answer 1

$a_n=59$

$a+(n-1)d=59$

$2+(n-1)(5-2)=59$

$3(n-1)=59-2=57$

$n-1=\frac{57}{3}=19$

$n=19+1=20$

Substitute the above value of $n$ in the formula for $S_n$:

$S_n=\frac{n}{2}(a+a_n)$

$S_n=\frac{n}{2}(a+a_n)$

$S_n=10\times 61=610$

Hence, the sum of the given terms is $\text{610}$.