Question

Which of the following is the explicit rule for the sequence -3, 5, 13, 21 ... *

Answer 1

`a_(n)` = 8n - 11

Explanation:

There is a common difference between consecutive terms in the sequence, that is

5 - (- 3) = 13 - 5 = 21 - 13 = 8

This indicates the sequence is arithmetic with n th term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 3 and d = 8 , thus

`a_(n)` = - 3 + 8(n - 1) = - 3 + 8n - 8 = 8n - 11 ← note this is the second option, that is

f(n) = - 3 + 8(n - 1)