How do I find the common difference with a term from the sequence and one from the series?

Question

So the question is this:

"If s is an arithmetic sequence (with associated series S) such that s₂₈ = -101 and S₄ = 4, find s₁₁ and S₂₀."

I am having difficulty finding the common difference in the sequence because I don't know how to use a term from the sequence and a term from the series to find what I am looking for.

Answer 1

S₂₈ = (28/2)[2a₁ + 27d]

-101 = 14[2a₁ + 27d]

-101 = 28a₁ + 378d

S₄ = (4/2){2a₁ + 3d]

4 = 2[2a₁ + 3d]

4 = 4a₁ + 6d

Solve the system for d.

Then use d in either (I'd do second equation) to deteremine a₁.

Can you deteremine S₁₁ and S₂₀?

Answer 2

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