MATH SOLVE

4 months ago

Q:
# 81, 27, 9, 3,... Find the common ratio of the given sequence, and write an exponential function which represents the sequence. Use n = 1, 2, 3, ... A) 3; f(n) = 81^n-1 B) 3; f(n) = 81(3)^n-1 C) 1 /3 ; f(n) = 81(3)^n-1 D) 1/ 3 ; f(n) = 81(1 /3 )^n-1Answer -Since each term is multiplied by 1/3to get to the next term, the common ratio is 1/3. The common ratio is also the base of anexponential function. The correct answer is1/3; f(n) = 81(1/3)^n-1so D.

Accepted Solution

A:

Given Sequence:

81, 27, 9 , 3 , ...

To find the common ratio:

Common ratio, r = a2/a1

r= 27/81

r=1/3

r= a3/a2= 9/27 = 1/3

r= a4/a3 = 3/9 = 1/3

So common ratio is 1/3.

Now exponential function is:

f(n) = 81 ( 1/3 )^(n-1)

When n=1

f(1)= 81 ( 1/3) ^ (1-1)

f(1)=81 ( 1/3)^0

f(1)=81(1) =81

When n=2

f(2)= 81 (1/3) ^(2-1)

f(2)= 81(1/3)^1

f(2)=27

And so on.

Answer: Option D. r= 1/3 , f(n)= 81 (1/3)^n-1

81, 27, 9 , 3 , ...

To find the common ratio:

Common ratio, r = a2/a1

r= 27/81

r=1/3

r= a3/a2= 9/27 = 1/3

r= a4/a3 = 3/9 = 1/3

So common ratio is 1/3.

Now exponential function is:

f(n) = 81 ( 1/3 )^(n-1)

When n=1

f(1)= 81 ( 1/3) ^ (1-1)

f(1)=81 ( 1/3)^0

f(1)=81(1) =81

When n=2

f(2)= 81 (1/3) ^(2-1)

f(2)= 81(1/3)^1

f(2)=27

And so on.

Answer: Option D. r= 1/3 , f(n)= 81 (1/3)^n-1