Official papers

Official 2022 Paper 1 · Q8

Paper 1Sequences & seriesNumber & counting

A geometric sequence has first term aa and common ratio rr, where aa and rr are positive integers and rr is greater than 1.

The sum of the first nn terms of this sequence is denoted by SnS_n.

It is given that the terms of the sequence satisfy

S30−S20=kS10S_{30}-S_{20}=kS_{10}

for some positive integer kk.

What is the smallest possible value of kk?

A2102^{10}
B2202^{20}
C2302^{30}
D210210−1\dfrac{2^{10}}{2^{10}-1}
E210(210−1)2^{10}(2^{10}-1)

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