Question 0420

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

Question

(a)
The 1st term of an arithmetic series is 9{9} and the 5th term is 5.{5.}
(ai)
Find the 37th term of the series.
[2]
(aii)
Find the sum of the 31st term to the 40th term inclusive of the series.
[3]
(b)
The 1st term of a geometric series is 9{9} and the 5th term is 4096729{\frac{4096}{729}} 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 7371100{\frac{7371}{100}}, show that
(89)n<0.09.\left(\frac{8}{9}\right)^n < 0.09.
Hence find the smallest possible value of n.{n.}
[5]

Answer