Question

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

Answer 1

Solution:

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;

$\begin{gathered} r=\frac{a_2}{a_1} \\ \\ r=\frac{2}{4}=\frac{1}{2} \\ \\ r=0.5 \end{gathered}$

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