Target Mathematics

3.11: AP sum inequality and geometric progression

0606/12/M/J/21 — Question 9 · 10 marks

(a)
The first three terms of an AP are −4-4, 88, 2020. Find the smallest nn for which the sum exceeds 20002000.
[4]
(b)(i)
The 77th and 99th terms of a GP are 2727 and 243243. Given r>0r>0, find rr.
[2]
(b)(ii)
Find the 3030th term as a power of 33.
[2]
(c)
Explain why 1,sin⁡θ,sin⁡2θ,…1,\sin\theta,\sin^{2}\theta,\ldots for −π2<θ<π2-\tfrac{\pi}{2}<\theta<\tfrac{\pi}{2} has a sum to infinity.
[2]