Question 0420

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

Question

(a)
The 1st term of an arithmetic series is 5{5} and the 4th term is 3.{3.}
(ai)
Find the 27th term of the series.
[2]
(aii)
Find the sum of the 71st term to the 90th term inclusive of the series.
[3]
(b)
The 1st term of a geometric series is 5{5} and the 4th term is 625216{\frac{625}{216}} 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 26.4{26.4}, show that
(56)n<0.12.\left(\frac{5}{6}\right)^n < 0.12.
Hence find the smallest possible value of n.{n.}
[5]

Answer