Question

Hey! I need some help with this equation.

Which function models the geometric sequence in the table?
n 1 2 3 4 5 <-- This is a table
an 75 15 3 3/5 3/25 <---
A. f(n)=75 (1/5) ^n
B. f(n)=5 (n) ^1/5
C. f(n)=75 (1/5) ^n−1

Answer 1

C. f(n)=75 (1/5) ^n-1

Explanation:

We see that each value in the table is 1/5 of the preceding value. 1-1 =0 the exponent we need to get 75 as the output.

1/5⁰ × 75 = 75 Any number to power⁰ is 1

When n is 2, again we need the exponent to be one less:

1/5¹ × 75 = 15 [75/5 =15]

1/5² × 75 = 3. [75/25 =3]

1/5³ × 75 = 3/5. 75/125 = 3/5

You see the pattern. You can keep calculating to verify.

The exponent will be n-1