Question

Write down an expression for the nth term of the following sequence

5, 11, 17, 23, ...

Answer 1

6n-1
Because:
6n= 6,12,18,24
6n-1=6x1-1=5,6x2-1=11,6x3-1=17 and 6x4-1=23

Answer 2

`a_(n)` = 6n - 1

Explanation:

There is a common difference d between consecutive terms in the sequence

d = 11 - 5 = 17 - 11 = 23 - 17 = 6

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 = 5 and d = 6 , then

`a_(n)` = 5 + 6(n - 1) = 5 + 6n - 6 = 6n - 1