Question

What is the first term of the arithmetic sequence with a recursive formula f(n) = f(n-1) + 3 and the rate of change 3, 6, 9, 12, 15, 18, 21, 24?

1) 3
2) 6
3) 9
4) 12

Answer 1

The first term of an arithmetic sequence with a recursive formula and a given rate of change cannot be determined without the initial term.

Step-by-step explanation:

The first term of an arithmetic sequence with a recursive formula f(n) = f(n-1) + 3 and a rate of change of 3, 6, 9, 12, 15, 18, 21, 24 can be found by substituting the given information into the recursive formula.

Since the rate of change is 3, the first term of the sequence is the initial term, f(1). We can plug in the values as follows:

f(1) = f(1-1) + 3 = f(0) + 3

Since the first term is the initial term, f(0), we need to find its value. There is no specific information given for f(0), so we cannot determine the first term using the recursive formula and the rate of change alone.