Question

1. a specific arithmetic sequence is defined by the function $f(x + 1) = \frac{5}{2}f(x)$ for $x \geq 1$. when $f(1) = 36$, what is the value of $f(5)$?

a. 1406.25
b. 562.5
c. 225
d. 90

Explanation:

Step1: Find f(2)

Given \( f(x + 1)=\frac{5}{2}f(x) \) and \( f(1) = 36 \). For \( x = 1 \), \( f(2)=\frac{5}{2}f(1)=\frac{5}{2}\times36 = 90 \).

Step2: Find f(3)

For \( x = 2 \), \( f(3)=\frac{5}{2}f(2)=\frac{5}{2}\times90 = 225 \).

Step3: Find f(4)

For \( x = 3 \), \( f(4)=\frac{5}{2}f(3)=\frac{5}{2}\times225 = 562.5 \).

Step4: Find f(5)

For \( x = 4 \), \( f(5)=\frac{5}{2}f(4)=\frac{5}{2}\times562.5 = 1406.25 \).

Answer:

a. 1406.25