Question

What is the sum of the arithmetic sequence 174, 168, 162 …, if there are 37 terms?

Answer 1

Sum of the series is `2442`

Explanation:

Sum of an Arithmetic series

`{a,(a+d),(a+2d),...(a+(n-1)d)}` up to `n` terms is given by

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

where `a` is the first term and `d` is the difference between a term and its preceding term.

Here first term `a=174` and `d=168-174=-6` and `n=37`

Hence the desired sum is `37/2xx{2xx174+(37-1)xx(-6)}` or

`37/2xx(348-36xx6)` or `37/2xx(348-216)` or

`37/2xx132=2442`