TMUA 2022 Paper 1 Q8 — Worked Solution

P1·Sequences & Series, Indices, Logarithms & Exponentials·6.5Official · 2022 · Q8

geometric-seriesfactorisinginteger-power

A geometric sequence has first term

a

and common ratio

r

, where

a

and

r

are positive integers and

r

is greater than

1

.The sum of the first

n

terms of this sequence is denoted by

S_{n}

.It is given that the terms of the sequence satisfy

S_{30} - S_{20} = k S_{10}

for some positive integer

k

.What is the smallest possible value of

k

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