Question

What is the sum of the arithmetic sequence 135, 123, 111 …, if there are 34 terms?

Answer 1

Sum of the sequence is `-4284`.

Explanation:

We have to find the sum of arithmetic sequence `{135, 123, 111 …}` up to 34 terms.

In the sequence `a_1, a_2, a_3, .... ... ,a_n` nth term is given by `a_1+(n-1)d` where `a_1` is the first term `d` is the constant difference (a_2-a_1). Here `a_1` is `135` and `d=-12`, hence

`a_34 = 135+33*(-12)= 135-396 = -261`.

Sum of the series is given by `n(a_1+a_n)/2` and in this case it turns out to be `34*(135-261)` or `34*(-126)` or `-4284`-