TMUA Euclid Sample Paper 2 · Question 3

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Euclid Sample Paper 2 · Q3

Paper 2Sequences & seriesNumber & counting

A sequence satisfies

a_{n+1}=1-a_n

for every positive integer $n$ . Consider

$P:$ The sequence has least period $2$ ,

$Q:$ $a_1\neq\frac12$ .

Which option correctly describes the relationship between $P$ and $Q$ ?

P

is necessary and sufficient for

Q

P

is sufficient but not necessary for

Q

P

is necessary but not sufficient for

Q

P

is neither necessary nor sufficient for

Q

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