1.5: A convergent geometric series

4PM1/2/June/2021 — Question 5 · 7 marks

The n\displaystyle nth term of a geometric series with common ratio r\displaystyle r is un\displaystyle u_n.
Given that
u2+u4=212.5andu3+u4=62.5,u_2+u_4=212.5 \qquad \text{and} \qquad u_3+u_4=62.5,
(a) find the two possible values of r\displaystyle r.
(5)
Given that the series is convergent with sum to infinity S\displaystyle S,
(b) find the exact value of S\displaystyle S.
(2)