Question 0420

Arithmetic and Geometric Progressions (APs, GPs)

2020 Paper 1 Question 8 Variant

Question

(a)

The 1st term of an arithmetic series is

{2}

and the 5th term is

{- 1.}

(ai)

Find the 23rd 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

{2}

and the 5th term is

{\frac{32}{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}

terms is greater than

{5.4}

, show that

\left(\frac{2}{3}\right)^n < 0.1.

Hence find the smallest possible value of

{n.}

[5]