Question 0420

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

Question

(a)
The 1st term of an arithmetic series is 7{7} and the 5th term is 15.{15.}
(ai)
Find the 33rd term of the series.
[2]
(aii)
Find the sum of the 51st term to the 80th term inclusive of the series.
[3]
(b)
The 1st term of a geometric series is 7{7} and the 5th term is 1296343{\frac{1296}{343}} 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 4851100{\frac{4851}{100}}, show that
(67)n<0.01.\left(\frac{6}{7}\right)^n < 0.01.
Hence find the smallest possible value of n.{n.}
[5]

Answer