Question

14/30 write an explicit formula for the sequence 45, 40, 35, 30, ... f(n) = f(1) + d(n - 1) or f(n) = f(1) · r^(n - 1). f(n) = 45 - 5(n - 1) f(n) = 45 · (8/5)^n f(n) = 5 - 45(n - 1) f(n) = 45 + 5(n - 1)

Explanation:

Step1: Identify sequence type

The sequence is 45, 40, 35, 30, ... . Check the difference between terms: \(40 - 45=-5\), \(35 - 40 = -5\), \(30 - 35=-5\). So it's an arithmetic sequence with first term \(f(1) = 45\) and common difference \(d=-5\).

Step2: Recall arithmetic sequence formula

The explicit formula for an arithmetic sequence is \(f(n)=f(1)+d(n - 1)\). Substitute \(f(1) = 45\) and \(d=-5\) into the formula: \(f(n)=45+(-5)(n - 1)=45 - 5(n - 1)\).

Answer:

\(f(n)=45 - 5(n - 1)\) (the first option among the given choices)