Caden's savings account accumulates interest at a constant rate of \(10%\) each year on the previous balance. This means that the amount in the account is multiplied by a fixed factor each year, specifically \(1 + 0.10 = 1.10\).
Given this characteristic, \(f(n)\) represents the balance after \(n\) years, which indicates that it is a geometric sequence. In a geometric sequence, each term is obtained by multiplying the previous term by a constant (in this case, \(1.10\)).
We can express the recursive formula for \(f(n)\):
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Starting value: \[ f(1) = 70 \]
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Recurrence relation for subsequent years: \[ f(n) = f(n-1) \times 1.10 \]
So, putting this together:
- Complete the statement: \[ f(1) = 70 \] \[ f(n) = f(n-1) \times 1.10 \]
Thus, the answer is: Choice B: Geometric sequence.