Answer:
(a) The sum of the previous term and 9
(b) 36, 45, 54
Step-by-step explanation:
Given
Sequence: Arithmetic Progression
[tex]0,9,18,27[/tex]
Solving (a): Describe the relationship in each term
First, we calculate the common difference (d)
In arithmetic progression:
[tex]d = T_n - T_{n-1}[/tex]
Take n as 2
[tex]d = T_2 - T_{2-1}[/tex]
[tex]d = T_2 - T_{1}[/tex]
Where
[tex]T_2 = 9\ and\ T_1 = 0[/tex]
[tex]d =9-0[/tex]
[tex]d =9[/tex]
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:
[tex]Next\ Term = 27 + 9 = 36[/tex]
[tex]Next = 36 + 9 = 45[/tex]
[tex]Next = 45 + 9 = 54[/tex]
Hence, the next three terms are: 36, 45 and 54
