Question

Answer each question based on the following arithmetic sequence:

11, 16, 21, 26,.........
Recursive Rule: f(n) = f(n-1) + d, n ≥ 2, given f(1).
Explicit Rule: f(n) = f(1) + d(n-1).
Part A:
For the sequence listed above, what is f(1)?
A) 11
B) 16
C) 21
D) 26
Part B:
For the sequence listed above, what is the common difference, d?
A) 3
B) 4
C) 5
D) 6
Part C:
For the sequence listed above, what is its recursive rule?
A) f(n) = f(n-1) + 5
B) f(n) = f(n-1) + 4
C) f(n) = f(n-1) + 3
D) f(n) = f(n-1) + 6

Answer 1

f(1), the first term of the sequence, is 11. The common difference, d, is 5. The recursive rule describing the sequence is f(n) = f(n-1) + 5.

Step-by-step explanation:

The student has provided an arithmetic sequence and is asked to identify specific elements of its relationships.

Part A: Identifying f(1)

f(1) represents the first term of the sequence. For the sequence 11, 16, 21, 26..., the first term is 11. Therefore, the correct answer is A) 11.

Part B: Finding the Common Difference

The common difference d is the amount added to each term to get the next term. In this sequence, each term increases by 5 (for example, 16 - 11 = 5), so the correct answer is C) 5.

Part C: Recursive Rule

The recursive rule for an arithmetic sequence is f(n) = f(n-1) + d. Since we've identified the common difference as 5, the correct recursive rule is A) f(n) = f(n-1) + 5.