contestada

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

Respuesta :

meerkat18
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:  The 10-th term of the sequence is [tex]\dfrac{4}{27}.[/tex]

Step-by-step explanation:  We are to find the 10-th term of a geometric sequence that has common ratio [tex]\dfrac{1}{3}[/tex] 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

[tex]a_n=a r^{n-1}.[/tex]

According to the given information, we have

[tex]r=\dfrac{1}{3},[/tex]

and

[tex]a_5=36\\\\\Rightarrow a r^{5-1}=36\\\\\Rightarrow ar^4=36\\\\\Rightarrow a\times \left(\dfrac{1}{3}\right)^4=36\\\\\Rightarrow a=36\times 81\\\\\Rightarrow a=2916.[/tex]

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

[tex]a_{10}=a r^{10-1}=2916\times r^9=2916\times \left(\dfrac{1}{3}\right)9\\\\\\\Rightarrow a_{10}=\dfrac{3^6\times 4}{3^9}\\\\\\\Rightarrow a_{10}=\dfrac{4}{27}.[/tex]

Thus, the 10-th term of the sequence is [tex]\dfrac{4}{27}.[/tex]