Question

What is the recursive rule for the sequence 54, 57, 60, 63, 66, ...?

a) f(1) = 54, f(n) = f(n − 1) + 3
b) f(1) = 54, f(n) = f(n − 1) + 4
c) f(1) = 54, f(n) = f(n − 1) + 5
d) f(1) = 54, f(n) = f(n − 1) + 6

Answer 1

The correct recursive rule for the sequence is f(1) = 54, f(n) = f(n − 1) + 3, which reflects the sequence's pattern of increasing by 3 from one term to the next.

Step-by-step explanation:

The recursive rule for the sequence 54, 57, 60, 63, 66, ... can be identified by analyzing the difference between consecutive terms. This sequence increases by 3 each time, which means that every term after the first is the previous term plus 3. Therefore, the recursive rule is:

f(1) = 54, f(n) = f(n − 1) + 3

This rule can be used to calculate any term in the sequence by taking the previous term and adding 3. To demonstrate, if we want to find the second term, we will use the first term and apply the rule:

f(2) = f(1) + 3 = 54 + 3 = 57

Similarly, for the third term:

f(3) = f(2) + 3 = 57 + 3 = 60

And so on for subsequent terms.