Nusret Balcı TMUA Paper 1 · Question 3

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Nusret Balcı TMUA Paper 1 · Q3

Paper 1Sequences & seriesNumber & counting

A geometric sequence has first term $a$ and common ratio $r$ , where $a$ and $r$ are positive integers and $r>1$ .

Define the alternating partial sums

A_n=a-ar+ar^2-ar^3+\cdots+(-1)^{n-1}ar^{n-1}.

It is given that

A_{20}=kA_{10}

for some positive integer $k$ .

What is the smallest possible value of $k$ ?

2^{10}

2^{10}-1

2^{10}+1

2^{20}+1

\frac{2^{10}+1}{2^{10}-1}

3^{10}+1

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