Question 0420

Arithmetic and Geometric Progressions (APs, GPs)

2020 Paper 1 Question 8 Variant

Question

(a)

The 1st term of an arithmetic series is

{8}

and the 8th term is

{13.}

(ai)

Find the 40th term of the series.

[2]

(aii)

Find the sum of the 31st term to the 90th term inclusive of the series.

[3]

(b)

The 1st term of a geometric series is

{8}

and the 8th term is

{\frac{823543}{262144}}

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

{\frac{1456}{25}}

, show that

\left(\frac{7}{8}\right)^n < 0.09.

Hence find the smallest possible value of

{n.}

[5]