1.29: The nth term of a geometric series is un

4PM1/2R/June/2019 — Question 7 · 11 marks

The nth term of a geometric series G\displaystyle G is un
The first term of G\displaystyle G is a and the common ratio of G\displaystyle G is J⋅\displaystyle {\mathit{J}}_{\cdot} where r⩾0\displaystyle r\geqslant0
Given that u3=4\displaystyle u3 = 4 and that u7=16\displaystyle u7 = 16
(a) (i) show that U=2\displaystyle U = 2
(ii) find the value of a.
(3)
(b) Find the least value of n\displaystyle n for which un 500\displaystyle 500
(4)
The sum of the first n\displaystyle n terms of G\displaystyle G is Sn
(c) Find Give your answer in the form p(1+2)\displaystyle p (1 + 2) where p\displaystyle p is an integer.
(4)