Question

Consider the geometric sequence: 1, 3, 9, 27, ...

Answer 1

Answer:

The answer is option D

Step-by-step explanation:

Since the sequence is a geometric sequence

For an nth term in a geometric sequence

$A(n) = a ({r})^{n - 1}$

where

n is the number of terms

a is the first term

r is the common ratio

To find n we must first find the common ratio

To find the common ratio divide the previous term by the next term

That's

r = 3/1 = 3 or r = 9/3 = 3

a = 1

Substitute the values into the above formula

That's

If n is an integer then

$A(n) = 1 ({3})^{n - 1}$

$A(n) = {3}^{n - 1}$

where n is greater than or equal to 2

Hope this helps you

Answer 2

Answer:

a

Step-by-step explanation:

if n=0

$a(n)=3^0=1 \\n=1\\a(n)=3^1=3\\n=2\\a(n)=3^2=9$

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a(n)=3^n,where~n ≥0