Question

How do you find the sum of the first 32 terms of the series `34+31+28+25+22...`?

Answer 1

The sum of the first `32` terms of the series is `-400`

Explanation:

As the terms in the series `34+31+28+25+22......` are constantly coming down starting from first term `34` by `3`,

this is an arithmetic series staring from `a=34` and `d=-3`

The sum of such a series up to `n` terms is

`n/2(2a+(n-1)d)`

Hence, the sum of the first `32` terms of the series is

`32/2xx(2xx34+(32-1)xx(-3))`

= `16xx(68-31xx3)`

= `16xx(68-93)`

= `16xx(-25)`

= `-400`