Question

What is the 10th term of the geometric sequence 400, 200, 100…?

A. 0.09765625
B. 0.390625
C. 0.78125
D. 1.5625

Answer 1

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

`a_n=ar^(n-1).`

In the given sequence,

first term, a = 400

and

common ration is given by

`r=(200)/(400)=(100)/(200)=~.~.~.~=0.5.`

Therefore, the 10th term of the sequence is

`a_(10)= ar^(10-1)=400* (0.5)^9=400*0.001953125=0.78125.`

Thus, the correct option is (C). 0.78125.