3.12: AP terms forming a geometric progression

0606/21/M/J/21 — Question 11 · 10 marks

(a)(i)
The 22nd, 88th and 4444th terms of an AP (first term 11, d>0d>0) form the first three terms of a GP.
Show that d=5d=5.
[5]
(a)(ii)
Find the sum of the first 2020 terms of the AP.
[2]
(b)(i)
Find the 55th term of the GP.
[2]
(b)(ii)
Explain whether the sum to infinity of this GP exists.
[1]