Precalculus, Chapter 9, 9.4, Section 9.4, Problem 55

The given sequence is:
5, 13 , 21 , 29, 37, 45
To determine if it is a linear sequence, take the difference between the consecutive terms.
5, 13, 21, 29, 37, 45
vvv vvv vvv vvv vvv
8 8 8 8 8
Since the difference between consecutive terms are the same, the given sequence is linear.
To determine the model of a linear sequence, apply the formula
a_n = a_1 + (n- 1)d
where an is the nth term, a1 is the first term, d is the common difference, and n is any positive integer.
Plugging in the values of a1 and d, the formula becomes:
a_n= 5 + (n-1)8
a_n=5 + 8n-8
a_n=8n - 3
Therefore, the given sequence can be represented by a linear model which is a_n=8n - 3 .