Question

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).

Answer 1

Answer:

$\dfrac{1}{216}$ = 0.005 (nearest thousandth)

Step-by-step explanation:

geometric series formula:  $a_n=ar^{n-1}$

where a is the first term and r is the common ratio

Given:

• $a_1=216$
• $a_2=36$
• $a_3=6$

$r=\dfrac{a_2}{a_1}=\dfrac{36}{216}=\dfrac16$

$\implies a_n=216 \cdot \dfrac16^{n-1}$

$\implies a_7=216 \cdot \dfrac16^{7-1}=\dfrac{1}{216}=0.005$