Question

PLEASE HELP ME. match the geometric sequence at the left with its explicit and recursive formulas at the right.

5, 20, 80, 320,….

Answer 1

The explicit and recursive formulas of 5, 20, 80, 320,…. are
`\text{f(n)} = \text{5} \cdot 4^{n-1` and f(n) = f(n - 1) * 4, where f(1) = 4, respectively

Match the geometric sequence with the explicit and recursive formulas

From the question, we have the following parameters that can be used in our computation:

5, 20, 80, 320,….

In the above sequence, we can see that 4 is multiplied to the previous term to get the new term

This means that

First term, a = 5

Common ratio, r = 4

It also means that the recursive sequence is

f(n) = f(n - 1) * 4, where f(1) = 4

Calculating the explicit formula, we have

`\text{f(n)} = \text{f(1)} \cdot r^{n-1`

Substitute the known values into the equation

`\text{f(n)} = \text{5} \cdot 4^{n-1`

Hence, the explicit and recursive formulas are
`\text{f(n)} = \text{5} \cdot 4^{n-1` and f(n) = f(n - 1) * 4, where f(1) = 4