Exercise 41 Page 205

First, we need to find the common difference of the arithmetic sequence. We are told that the

first

term

is

3

and that the

common

difference

is

1.5

times the

first

term .

d = 1.5 \times 3 = 4.5

By adding the

common

difference

to the

first

term,

we get the

second

term .

We can then use this information to find each consecutive term.

a_{1} 7.53 + 4.5 . . . = 3 a_{2} = 7.3 + 4.5 = 7.5 a_{3} = 7.5 + 4.5 = 12 a_{4} = . 12 + 4.5 = 16.5

To graph the sequence we have to write the terms as ordered pairs,

(n, a_{n}) .

Here,

n

is the position of the term and

a_{n}

is its value.

If we mark these points on a coordinate plane, we get the graph of the sequence.