Question

List the first five terms of the sequence. a1 = 4, an+1 = 5an − 3

Answer 1

The recursive formula

`a_(n+1) = 5a_n-3`

is telling you that the next term in the sequence is five times the previous one, minus 3.

So, if we start with
`a_1=4`, we have to multiply it by 5 and subtract 3 to get the next:

`a_2 = 5a_1-3 = 5\cdot 4 - 3 = 20-3 = 17`

And similarly we can obtain all the next terms:

`a_3 = 5a_2-3 = 5\cdot 17 - 3 = 85-3 = 82`

`a_4 = 5a_3-3 = 5\cdot 82 - 3 = 410-3 = 407`

`a_5 = 5a_4-3 = 5\cdot 407 - 3 = 2035-3 = 2032`