Answer: The correct option is (C). 0.78125.
Step-by-step explanation: We are given to find the 10th term of the following geometric sequence
400, 200, 100, . . . .
We know that,
the n-th term of a geometric sequence with first term a and common ration r is given by
[tex]a_n=ar^{n-1}.[/tex]
In the given sequence,
first term, a = 400
and
common ration is given by
[tex]r=\dfrac{200}{400}=\dfrac{100}{200}=~.~.~.~=0.5.[/tex]
Therefore, the 10th term of the sequence is
[tex]a_{10}= ar^{10-1}=400\times (0.5)^9=400\times0.001953125=0.78125.[/tex]
Thus, the correct option is (C). 0.78125.
