Final answer:
The tenth term of the geometric sequence with a common ratio of 1/3 and the fifth term 36 is found using the formula for the nth term in a geometric sequence. Upon calculating, we find that the tenth term is 4/81.
Step-by-step explanation:
The question asks for the tenth term of a geometric sequence with a common ratio of 1/3 and the fifth term being 36. In a geometric sequence, each term after the first is found by multiplying the previous term by the common ratio.
To find the nth term of a geometric sequence, the formula is:
an = a1 × r(n-1)
Where an is the nth term, a1 is the first term, and r is the common ratio.
We are given the fifth term (a5=36) and need to find the first term (a1). Using the fifth term, we have:
36 = a1× (1/3)(5-1)
36 = a1× (1/3)4
36 = a1× (1/81)
a1 = 36 × 81
Now that we have a1, we can calculate the tenth term (a10):
a10 = a1 × (1/3)(10-1)
a10 = 36 × 81 × (1/3)9
After simplifying the expression, we find the tenth term to be 4/81, which matches option C.