Find a recurrence relation satisfied by this sequence. a_{n}=2n

allhvasstH

allhvasstH

Answered question

2021-09-16

Find a recurrence relation satisfied by this sequence.
an=2n

Answer & Explanation

Laaibah Pitt

Laaibah Pitt

Skilled2021-09-17Added 98 answers

Given:
an=2n
Let us first determine the first term by replacing n in the given expression for an by 0:
a0=2(0)=0
Let us similarly the next few terms as well:
a1=2(1)=2=a0+2
a2=2(2)=4=a1+2
a3=2(3)=6=a2+2
We note that each term is the previous term increased by 2:
an=an1+2
Thus a recurrence relation for an is then:
a0=0
an=an1+2
Note: There are infinitely many different recurence relations that satisfy any sequence.

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