Originally Posted by

**Sithranio**
I'm going through some past exams and I came upon a question that I have absolutely no idea how to even start. I found the answer in a mark scheme but I have no idea how to get to it nor do I understand the working. It's probably something very simple but for some reason I have hit a blank.

Question:

An arithmetic progression has first term a and common difference d. It is given that the

sum of the first 200 terms is 4 times the sum of the first 100 terms.

a. Find d in terms of a.

b. Find the 100th term in terms of a.

Answer in mark scheme:

(i) 200/2(2a + 199d)

= 4 × 100/2(2a + 99d)d = 2a

(ii) a + 99d

= a + 99 × 2a

199a

An help with this would be deeply apreciated. Thank you in advance

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