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Ugo [173]
3 years ago
8

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

Mathematics
1 answer:
Shkiper50 [21]3 years ago
5 0

Answer:

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

Step-by-step 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

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