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
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