Question

The A.P. in which $8^{th}$ term is $-15$ and $9^{th}$ term is $-30$. Find the sum of the first $10$ numbers.

Answer 1

$8^{th}term=15$

$9^{th}term=30$

$a+7d=15$

$a+8d=30$

$d=15$

$a+105=15$

$a=-90$

sum of first 10 numbers

$=\frac{10}{2}(2x-90+(10-1\left)15\right)$

$=\frac{10}{2}(-180+135)$

$=5(-45)$

$=-225$