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.
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.
