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:

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

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

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