3.5: Geometric progression terms and arithmetic sum

0606/22/F/M/23 — Question 6 · 11 marks

(a)(i)
A geometric progression has first term 6464 and common ratio 0.50.5.
Find the 1010th term.
[2]
(a)(ii)
Find the sum of the first 1010 terms.
[2]
(a)(iii)
Find the sum to infinity.
[1]
(b)
An arithmetic progression is such that S20−400=2S10S_{20}-400=2S_{10} and u1:u6=1:5u_{1}:u_{6}=1:5.
Find the sum of the first 33 terms of this progression.
[6]