2
AssignmentMultiple Choice

Recursive Formulas

Question 2 • AZ-Common Core Algebra II B

Identify the recursive formula for the following sequence: 8, 26, 80, 242, . . .

Answer
A
an = an – 1 + 18 where a1 = 8
B
an = 3an – 1 + 2 where a1 = 8
C
an = 4an – 1 – 6 where a1 = 242
D
an = 8 + (n–1) · 18 where a1 = 18

Explanation

Each term is 3 times the previous term, then 2 is added: 8 × 3 + 2 = 26, 26 × 3 + 2 = 80, and 80 × 3 + 2 = 242. Thus the recursive formula is aₙ = 3aₙ₋₁ + 2 with a₁ = 8, which is choice B.

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