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-1

Answer -

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-1

so D.

Question

Mathematics

Ana Dillon

26 September, 02:56

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-1

Answer -

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-1

so D.

+5

Answers (1)

Know the Answer?

Nigel Goodwin · Answer 1

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