Question

Consider a sequence defined by the recursive rule f(1) = 15; f(n)=f(n - 1) - 6 for n 2. Choose True or

False for each statement.
The second term of the sequence is 8.
A
True
B
False
The third term of the sequence is 3.
True
A
B
False
The fourth term of the sequence is -3.
True
А
False
B

Answer 1

The second term of the sequence is 8 False ⇒ B

The third term of the sequence is 3 True ⇒ A

The fourth term of the sequence is -3 True ⇒ A

Explanation:

The form of the recursive rule is:

f(1) = first term; f(n) = f(n - 1) + d, where

• f(1) is the first term

• f(n) is the nth term

• f(n - 1) is the term before the nth term

• d is the common difference

∵ f(1) = 15, f(n) = f(n - 1) - 6 for n ≥ 2

∴ The first term = 15

∴ d = -6

let us find the 2nd, 3rd, and 4th terms

∵ n = 2

∴ f(2) = f(1) - 6

∵ f(1) = 15

∴ f(2) = 15 - 6 = 9

∴ The second term is 9

∴ The second term of the sequence is 8 False

∵ n = 3

∴ f(3) = f(2) - 6

∵ f(2) = 9

∴ f(3) = 9 - 6 = 3

∴ The third term is 3

∴ The third term of the sequence is 3 True

∵ n = 4

∴ f(4) = f(3) - 6

∵ f(3) = 3

∴ f(4) = 3 - 6 = -3

∴ The fourth term is -3

∴ The fourth term of the sequence is -3 True