Find a recurrence relation satisfied by this sequence. a_{n}=2n+3

Kyran Hudson

Kyran Hudson

Answered question

2021-09-23

Find a recurrence relation satisfied by this sequence.
an=2n+3

Answer & Explanation

Liyana Mansell

Liyana Mansell

Skilled2021-09-24Added 97 answers

Given:
an=2n+3
Let us first determine the first term by replacing n in the given expression for an by 0:
a0=2(0)+3=3
Let us similarly determine the next few terms as well:
a1=2(1)+3=5=a0+2
a2=2(2)+3=7=a1+2
a3=2(3)+3=9=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=3
an=an1+2
Note: There are infinitely many different recurence relations that satisfy any sequence.

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