Question

The first four terms of a sequence are: 8, 24, 72, 216, ... Write a recursive function for this sequence.

a) aₙ = aₙ₋₁ × 3
b) aₙ = aₙ₋₁ + 3
c) aₙ = aₙ₋₁ ÷ 3
d) aₙ = aₙ₋₁ - 3

Answer 1

The recursive function for the given sequence is option (a) aₙ = aₙ₋₁ × 3, as each term is three times the previous term.

Step-by-step explanation:

The sequence provided by the student is geometric in nature, where each term is a multiple of the previous term. To find the recursive function for the sequence, we need to establish the relationship between consecutive terms. Observing the sequence: 8, 24, 72, 216, ..., we see that each term is 3 times the previous term (24 is 8 multiplied by 3, 72 is 24 multiplied by 3, and so on). Therefore, the recursive function for this geometric sequence is a₅ = a₄ × 3, which means each term (from the second term onwards) is equal to the previous term multiplied by 3. Specifically, option (a) aₙ = aₙ₋₁ × 3 correctly represents this sequence.