Question

Identify the recursive formula for the following sequence: 8, 26, 80, 242, . . .

Answer 1

an = 3an – 1 + 2 where a1 = 8

Answer 2

Recursive formula is
`a_n = (a_(n-1) *3) + 2`

Explanation:

8, 26, 80, 242, . . .

8 is the first term

To get 26 we multiply 8 by 3 and then add 2

8*3 = 24 + 2= 26

26 * 3= 78+2 = 80

80*3 = 240 + 2 = 242

So to get next term we multiply the previous term by 3 and then we add 2

`a_n = (a_(n-1) *3) + 2`