use the arithmetic summation formula to find the sum of the series: -6+2+2+...+58

Question

I know how to solve these types of questions, but I can't find a common ratio/difference because it's +2+2.

Answer 1

If the given sum is correct, then we don't have a sum from an arithmetic series. If the sum is supposed to be part of an arithmetic series, then perhaps it should be -6+2+10+18+26+34+42+50+58. In that case, the common difference, d, is 8.

The nth term would be a_n = a₁ + (n-1)d = -6 + 8(n-1) = 8n - 14.

If 8n - 14 = 58, then n = 9.

So, -6+2+10+...+58 = S₉ = (9/2)(a₁ + a₉) = (9/2)(-6+58) = 234.