Precalculus, Chapter 9, 9.4, Section 9.4, Problem 56

Firstly we need to determine whether the series is linear or quadratic. A linear sequence is a sequence of numbers in which there is a first difference between any consecutive terms is constant. However, a quadratic sequence is a sequence of numbers in which there is a second difference between any consecutive terms is constant.
Now let's determine if the above sequence is linear or quadratic.
Lets begin by finding the first difference:
T_2 - T_1 = 9 - 2 = 7
T_3 - T_2 = 16 - 9 = 7
T_4 - T_3 = 23 - 16 = 7
From above we can see we have a constant number for the first difference, hence our sequence is linear.
Now let's determine the model of this sequence. The equation of a linear sequence is as follows:
T_n = a + d(n-1)
Where
T_n = Value of the term in sequence
a = first number of sequence
d = common difference (first difference)
n = term number
Now let's substitute values into the above equation:
T_n = 2 + 7(n-1)
T_n = 2 + 7n - 7
The model is simplified to:
T_n = 7n -5

Now let's double check our model using terms 1, 3 and 6:
T_1 = 7(1) - 5 =2
T_3 = 7(3) - 5 = 16
T_7 = 7(6) - 5 = 37
Summary:
The sequence is linear.
Model:
T_n = 7n - 5