TMUA Viluxent Set 1 Paper 2 · Question 7

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Viluxent Set 1 Paper 2 · Q7

Paper 2Logic & proofSequences & series

A sequence is defined by $a_1=k$ , for some real number $k$ , and

a_{n+1}=a_n^2-2\qquad(n\ge1).

$P$ : The sequence $(a_n)$ is bounded. $Q$ : $-2\le k\le2$ .

Which one of the following is true?

P

is neither necessary nor sufficient for

Q

P

is sufficient but not necessary for

Q

P

is necessary and sufficient for

Q

P

is necessary but not sufficient for

Q

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