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Can you help me with this A2 maths question/s?

Well here is:

A geometric series has first term a and common ratio r. the third term = 24 and the sum of the second, third and fourth terms = -56.

1) show that r satisfies:
3r^2 + 10r + 3 = 0

2) given | r | < 1 find the value of r and sum to infinity of the series

all for 8 marks. I’m pretty stuck and I can’t really find a worked answer in my notes I can springboard off of. I’ve tried a few ways but I’m stumped. Would someone be able to give me a worked answer so I can understand and answer more questions like this future?

Reply 1

nerak99

The first three terms are a, ar and ar^2 and they add to 24. This allows to write down a quadratic equation which you can put into the standard form of a we and solve. Hope that helps