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

User Jan Franta
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Answer:


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

Step-by-step 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:


(100)/(20)\text{ = }(500)/(100)\text{ = }(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

User Martin Kouba
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