Suppose that T= ar^n-1 is a GP with a limiting sum.

Question

a) Find the common ratio r if the limiting sum equals 5 times the first term. (Answer: r=4/5)

b) Find the ratio if the sum of all terms except the first equals 5 times the first term. (Answer: 5/6)

Thanks so much to anyone who helps

Answer 1

If S = 5 times the 1st, then
a/(1-r) = 5a
solve for r.

If the 1st term is excluded, then
a/(1-r) - a = 5a