Question 0420

Arithmetic and Geometric Progressions (APs, GPs)
2020 Paper 1 Question 8 Variant

Question

(a)
The 1st term of an arithmetic series is 8{8} and the 3rd term is 3.{3.}
(ai)
Find the 45th term of the series.
[2]
(aii)
Find the sum of the 21st term to the 60th term inclusive of the series.
[3]
(b)
The 1st term of a geometric series is 8{8} and the 3rd term is 51281{\frac{512}{81}} where the common ratio is positive.
(bi)
Find the sum to infinity of the series.
[2]
(bii)
Given that the sum of the first n{n} terms is greater than 61.2{61.2}, show that
(89)n<0.15.\left(\frac{8}{9}\right)^n < 0.15.
Hence find the smallest possible value of n.{n.}
[5]

Answer