4
AssignmentMultiple Choice

Recursive Formulas

Question 4 • AZ-Common Core Algebra II B

The third term in an arithmetic sequence is 3, and the common difference between each term is 4. Write a recursive formula for the sequence.

Answer
A
an = 4an – 1 where a3 = 3
B
an = an – 1 + 4 where a3 = 3
C
an = an – 1 + 4 where a1 = 3
D
an = 3 + (n – 1) · 4 where a3 = 3

Explanation

A recursive formula gives each term using the term immediately before it. Since the common difference is 4, add 4 each time: aₙ = aₙ₋₁ + 4. The given third term is a₃ = 3, so choice B, aₙ = aₙ₋₁ + 4 where a₃ = 3, is correct.

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