2.8: Geometric and arithmetic progressions

0606/22/M/J/20 — Question 10 · 11 marks

The first 5 terms of a sequence are given below.
4−21−0.50.254 \quad -2 \quad 1 \quad -0.5 \quad 0.25
(a)(i)
Find the 20th term of the sequence.
[2]
(a)(ii)
Explain why the sum to infinity exists for this sequence and find the value of this sum.
[2]
(b)(i)
The tenth term of an arithmetic progression is 15 times the second term. The sum of the first 6 terms of the progression is 87.
Find the common difference of the progression.
[4]
(b)(ii)
For this progression, the nnth term is 6990. Find the value of nn.
[3]