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jernplate8

Answered question

2021-09-08

Find a recurrence relation satisfied by this sequence.

a_{n} = 5^{n}

krolaniaN

Skilled2021-09-09Added 86 answers

Given:

a_{n} = 5^{n}

Let us first determine the first term by replacing n in the given expression for

a_{n}

by 0:

a_{0} = 5^{0} = 1

Let us similarly determine the next few terms as well:

a_{1} = 5^{1} = 5 = 5 a_{0}

a_{2} = 5^{2} = 25 = 5 a_{1}

a_{3} = 5^{3} = 125 = 5 a_{2}

We note that each term is the previous term multiplied by 5:

a_{n} = 5 a_{n - 1}

Thus a recurrence relation for

a_{n}

is then:

a_{0} = 1

a_{n} = 5 a_{n - 1}

Note: There are infinitely many different recurence relations that satisfy any sequence.

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