Question

Given the sequence: 1, 3, 9, -

Complete the formula by using the drop-down boxes. The recursive formula will be f(n) = f(n-1)

a) × 3
b) + 6
c) - 6
d) × 2

Answer 1

The recursive formula for the sequence 1, 3, 9 is f(n) = f(n-1) × 3, which describes multiplying the preceding term by 3 to obtain the next term.

Step-by-step explanation:

The student is asking for the recursive formula that represents the given sequence: 1, 3, 9. To determine the correct operation needed to transition from one term to the next, we examine the pattern present in the sequence.

Starting with 1 and moving to the subsequent number, 3, we see that it is a result of multiplying by 3 (1 × 3 = 3). Similarly, moving from 3 to 9 also involves a multiplication by 3 (3 × 3 = 9). Therefore, the recursive formula is f(n) = f(n-1) × 3, where f(n) denotes the nth term in the sequence.

This formula accurately represents the process of finding any term in the sequence by multiplying the previous term by 3.