Question

What is the tenth term of the geometric sequence that has a common ratio of 1/3 and 36 as its fifth term?

a. 4/7
b. 27/4
c. 4/81
d. 1/36

Answer 1

Base on the question or the problem which ask to choose among the following choices that states, what would be the tenth term of the geometric sequence that has a common ration of 1/2 and 36 as it's fifth term, base on the question, I would say that the answer would be letter 4/27. I hope this would help 

Answer 2

Answer: The 10-th term of the sequence is
`(4)/(27).`

Step-by-step explanation: We are to find the 10-th term of a geometric sequence that has common ratio
`(1)/(3)` and fifth term is 36.

We know that the n-th term of a geometric sequence with first-term 'a' and common ratio 'r' is given by

`a_n=a r^(n-1).`

According to the given information, we have

`r=(1)/(3),`

and

`a_5=36\\\\\Rightarrow a r^(5-1)=36\\\\\Rightarrow ar^4=36\\\\\Rightarrow a* \left((1)/(3)\right)^4=36\\\\\Rightarrow a=36* 81\\\\\Rightarrow a=2916.`

Therefore, the 10-th term of the sequence will be

`a_(10)=a r^(10-1)=2916* r^9=2916* \left((1)/(3)\right)9\\\\\\\Rightarrow a_(10)=(3^6* 4)/(3^9)\\\\\\\Rightarrow a_(10)=(4)/(27).`

Thus, the 10-th term of the sequence is
`(4)/(27).`