Question

Convert each geometric sequence into an exponential function. 4, 20, 100, 500,….

Answer 1

Answer:

$\text{ a}_n=4\cdot(5)^n$

Explanation:

here, we want to convert the given geometric sequence into an exponential function

We have the exponential function generally as:

$y=ab^x$

with respect to the geometric sequence, it will be in the form:

$\text{ y = ar}^n$

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

Looking at the given arrangement, 4 is the first term

Now, we can get the common ratio by dividing subsequent terms

Mathematically, we have that as:

$\frac{100}{20}\text{ = }\frac{500}{100}\text{ = }\frac{20}{4}\text{ = 5}$

So, we have the first term as 4 and the common ratio as 5

Thus, we have the exponential function as:

$\text{ a}_n=4\cdot(5)^n$

where n is the term number