Question

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

Answer 1

Answer:

(a) The sum of the previous term and 9

(b) 36, 45, 54

Step-by-step 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