1.17: Past-paper question 8

4PM1/1/June/2024 — Question 8 · 12 marks

The sum of the first and second terms of a geometric series G\displaystyle G is 400
The sum of the second and third terms of G\displaystyle G is 100
(a) Show that the common ratio of G\displaystyle G is 14\displaystyle \frac{1}{4}
(4)
(b) Show that the first term of G\displaystyle G is 320
(2)
(c) Find the sum to infinity of G\displaystyle G
(2)
The sum to n\displaystyle n terms of G\displaystyle G is Sn\displaystyle S_n
(d) Find, using logarithms, the least value of n\displaystyle n such that
Sn>426.6S_n > 426.6
(4)