Question

Which of the following is the explicit rule for a geometric sequence defined by a recursive formula of (aⁿ = 13aⁿ⁻¹) for which the first term is 7?

a) (aₙ = 7 × 13ⁿ)
b) (aₙ = 7 × 13ⁿ⁻¹)
c) (aₙ = 7ⁿ + 13)
d) (aₙ = 7ⁿ × 13)

Answer 1

The explicit rule for the geometric sequence defined by the recursive formula aⁿ = 13aⁿ⁻¹ with the first term being 7 is b) aₙ = 7 × 13ⁿ⁻¹.

Step-by-step explanation:

The question is asking for the explicit rule of a geometric sequence with a recursive formula aⁿ = 13aⁿ⁻¹, where the first term is 7. To find the explicit formula, we start with the first term, which we'll call a₁, and then multiply it by the common ratio (13) raised to the power of (n-1), since each subsequent term is generated by multiplying the previous term by 13.

The explicit rule for the geometric sequence is therefore (b) aₙ = 7 × 13ⁿ⁻¹, which shows that each term (aₙ) is equal to the first term (7) multiplied by 13 raised to the power of (n-1).