Question

Find the sum of the first 40 terms of the series (-59)+(-56)+(-53)+…..

Answer 1

Given:

`(-59)+(-56)+(-53)+\text{.}\ldots\ldots\text{.}`

The given series is in arithmetic progression with a common difference of 3.

The sum of the first n terms in the arithmetic progression is given as,

`\begin{gathered} S_n=(n)/(2)\lbrack2a+(n-1)d\rbrack \\ a=-59,d=3 \\ S_(40)=(40)/(2)\lbrack2(-59)+(40-1)3\rbrack \\ =20\lbrack-118+117\rbrack \\ =-20 \end{gathered}`

Answer: the sum of the first 40 terms in the given series is -20.