TMUA Viluxent Set 1 Paper 2 · Question 16

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Viluxent Set 1 Paper 2 · Q16

Paper 2Logic & proofSequences & seriesNumber & counting

A sequence satisfies $a_1=a_2=1$ and $a_{n+2}=a_{n+1}+a_n+1$ for $n\ge1$ .

(I) $a_n$ is odd for every positive integer $n$ .

(II) $a_n+1$ is a power of $2$ for every positive integer $n$ .

(III) $a_{n+3}-a_n$ is even for every positive integer $n$ .

Which of these statements are true?

A(I) only

B(II) only

C(III) only

D(I) and (II) only

E(I) and (III) only

F(II) and (III) only

Gall of them

Hnone of them

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