TMUA Beyond Horizon Set 1 Paper 2 · Question 5

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Beyond Horizon Set 1 Paper 2 · Q5

Paper 2Sequences & seriesNumber & counting

Consider the sequence: $a_1=101$ , $a_2=10101$ , $a_3=1010101$ , $\ldots$ . Then $a_k$ is a composite number (that is, not a prime number):

Aif and only if

k\ge 2

and

11

divides

10^{k+1}+1

;

Bif and only if

k\ge 2

and

11

divides

10^{k+1}-1

;

Cif and only if

k\ge 2

and

k-2

is divisible by

3

;

Dif and only if

k\ge 2

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