Find the first six terms of the sequence defined by each of these recurrence relations and initial conditions.a) an = (an−1)2 , a1 = 2 ( Just find its general formula )

Khaleesi Herbert

Khaleesi Herbert

Answered question

2021-02-05

Determine the first six terms of the sequence defined by each of these recurrence relations and initial conditions.
a) an=(an1)2, a1=2 ( Just find its general formula )

Answer & Explanation

Aamina Herring

Aamina Herring

Skilled2021-02-06Added 85 answers

So, the given recurrence relation is: an=2an1, a1=2
Then we note that:
a1=2
a2=2a1=22=4=22
a3=2a2=24=8=23
a4=2a3=28=16=24
a5=2a4=216=32=25
a6=2a5=232=64=26
Therefore we find the general term is an=2n, for nN. Prove: Note that
an=2an1=22an2=22an2==2n1a1=2n

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