Question 0420

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

Question

(a)
The 1st term of an arithmetic series is 6{6} and the 6th term is 12.{12.}
(ai)
Find the 14th term of the series.
[2]
(aii)
Find the sum of the 51st term to the 60th term inclusive of the series.
[3]
(b)
The 1st term of a geometric series is 6{6} and the 6th term is 61443125{\frac{6144}{3125}} 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 28.2{28.2}, show that
0.8n<0.06.0.8^n < 0.06.
Hence find the smallest possible value of n.{n.}
[5]

Answer