Question

What is the value of the next term in the geometric sequence graphed below?A. 0.125B. 4C. 2D. 0.25

Answer 1

In the geometric sequence graphed below;

The sequence in list form is;

`4,2,1,0.5,...`

The first term is 4, and the common ratio, r, is;

`\begin{gathered} r=(a_2)/(a_1) \\ \\ r=(2)/(4)=(1)/(2) \\ \\ r=0.5 \end{gathered}`

0.5The nth term of a geometric sequence is;

`a_n=ar^(n-1)`

Thus, the fifth term of the sequence is;

`\begin{gathered} n=5; \\ \\ a_5=4(0.5)^(5-1) \\ \\ a_5=4(0.5)^4 \\ \\ a_5=0.25 \end{gathered}`

CORRECT OPTION: (D) 0.25