Find the sum of 
$1+4+7+10+.....$ to $22$ terms

Consider the given series

$1+4+7+10+......to22terms.$,

Ferst , second third terms are

$t_1=1$

$t_2=4$

$t_3=7$

Now,

$t_2-t_1=t_3-t_2$

$4-1=7-4$

$3=3$

Hence, given series is A.P.

Where, number of term $n=22$

Common difference is $d=3$

Now,

Sum of given series is

$s_{22}=\frac{22}{2}[2\times 1+\left(22-1\right)3]$

$=11\left(2+21\times 3\right)$

$=11\times 65$

$=715$

Hence, this is the answer.