Question

Find the sum of the first 30 terms of the arithmetic sequence 10, 18, 26...

Answer 1

Given the sequence 10,18,26....

$\Rightarrow \text{First term,}{a}_1=10\text{Common difference,}d=a_2-a_1$

$=18-10$

$=8$

$\because a_n=a_1+(n-1)d\Rightarrow a_{30}=a_1+29d$

$=10+29\left(8\right)$

$=10+232$

$=242$

$S_n=\frac{n}{2}(a+l),$ where '$a$' is the first term and '$l$' is the last term.

$\therefore S_{30}=\frac{n}{2}(a_1+a_{30})$

$=\frac{30}{2}(10+242)=15\left(252\right)$

$=3780$