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AssignmentMultiple Choice

Writing Linear Equations

Question 4 • AZ-Algebra 1A (MA101)

Which sequence can be defined by the recursive formula f (1) = 4, f (n + 1) = f (n) – 1.25 for n ≥ 1?

Answer
A
1, –0.25, –1.5, –2.75, –4, . . .
B
1, 2.25, 3.5, 4.75, 6, . . .
C
4, 2.75, 1.5, 0.25, –1, . . .
D
4, 5.25, 6.5, 7.75, 8, . . .

Explanation

The first term is f(1) = 4. Each next term is 1.25 less than the previous term: 4 − 1.25 = 2.75, then 2.75 − 1.25 = 1.5, then 1.5 − 1.25 = 0.25, and then 0.25 − 1.25 = −1. This matches the sequence 4, 2.75, 1.5, 0.25, −1, . . . .

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