Question

Convert each geometric sequence into an exponential function.-4, -16, -64, -256,…

Answer 1

`\text{ a}_n=-4\cdot(4)^(n-1)`

Step-by-step explanation:

The general exponential form of terms in an exponential sequence is:

`\text{ a}_n=ar^(n-1)`

where a is the first term, r is the common ratio and n is the term number

We already have the first term as -4

To get the common ratio, we have to divide subsequent terms as follows:

`r\text{ = }(-16)/(-4)\text{ = }(-64)/(-16)\text{ = }(-256)/(-64)\text{ = 4}`

Thus, we have the exponential function as:

`\text{ a}_n=-4\cdot(4)^(n-1)`