Arithmetic Sequence Question. Help!

Question

What is the sum of the first 13 terms of the arithmetic sequence which has a11 = 25 and a20 = 70?

Answer 1

Since there are nine steps from a₁₁ to a₂₀, we do (70 - 25)/9 = 45/9 = 5

Now we know the common difference is 5.

And since there are 2 steps from a₁₁ to a₁₃, a₁₃ = 35

Ten steps back ward gives us a₁ = -25

SUM = (n/2)(a₁ + a_n) = (13/2)(-25 + 35) = 65

I hope that helps. Let me know if you need more explanation.