Question

If a1=9 and an=an-1+4 then find the value of a5

Answer 1

25

is the answer

just find the a0 first

Answer 2

`\sf a_5 =25`

Explanation:

Definition:

A recurrence relation is a mathematical equation that defines the terms of a sequence by relating each term to the previous terms.

The given recurrence relation is
`\sf a_n = a_(n-1) + 4` with initial condition
`\sf a_1 = 9` . This means that the first term of the sequence is 9 and each subsequent term is equal to the previous term plus 4.

In order to find the value of a5, we can simply apply the recurrence relation four times:

`\sf a_2 = a_1 + 4 = 9 + 4 = 13`

`\sf a_3 = a_2 + 4 = 13 + 4 = 17`

`\sf a_4 = a_3 + 4 = 17 + 4 = 21`

`\sf a_5 = a_4 + 4 = 21 + 4 = 25`

Therefore, the value of
`\sf a_5` is 25.