Question

Describe the relationship between the terms in each arithmetic sequence. Then

write the next three terms in each sequence. (Examples 1 and 2)

Answer 1

(a) The sum of the previous term and 9

(b) 36, 45, 54

Explanation:

Given

Sequence: Arithmetic Progression

`0,9,18,27`

Solving (a): Describe the relationship in each term

First, we calculate the common difference (d)

In arithmetic progression:

`d = T_n - T_(n-1)`

Take n as 2

`d = T_2 - T_(2-1)`

`d = T_2 - T_(1)`

Where

`T_2 = 9\ and\ T_1 = 0`

`d =9-0`

`d =9`

The relationship is: The sum of the previous term and 9

Solving (b): The next three terms

As said in (a) each term is derived from a sum of 9 and the previous term

So, we have:

`Next\ Term = 27 + 9 = 36`

`Next = 36 + 9 = 45`

`Next = 45 + 9 = 54`

Hence, the next three terms are: 36, 45 and 54