Question

Given the first five terms of the sequence an=2, 6, 18, 54, 162 . . .
, determine which option is the correct subscript notation for the recursive formula.

Option #1: a1=2
; an=3an−1


Option #2: a1=2
; an=3an+1


Option #3: a1=2
; an=3an−1+2

Answer 1

Correct answer: Option #1.

Reason: The sequence multiplies by 3 each step, so a1 = 2 and a_n = 3 a_{n-1}. Check: a2 = 3·2 = 6, a3 = 3·6 = 18, etc. Options #2 and #3 give incorrect index or an extra +2.