Question

How do you find the sum of the first 40 terms of the series `50+42+34+26+18+...`?

Answer 1

Sum of first 40 terms of the given series is `-4240`

Explanation:

The series `50+42+34+26+18+...........` is arithmetic series whose fist term is `a` and difference between a term and its immediate preceding term is `-8`.

In an arithmetic series, whose first term is `a` and difference between a term and its immediate preceding term is `d`

`n^(th)` term is `a+(n-1)d` and

sum of first `n` terms is `n/2(2a+(n-1)d)`

Hence sum of first 40 terms of the given series is

`40/2xx(2xx50+(40-1)xx(-8))`

= `20xx(100+39xx(-8))=20xx(100-312)`

= `20xx(-212)=-4240`