Question

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

216
,
36
,
6
,
.
.
.
216,36,6,...
Find the 7th term.
Find the 7th

Answer 1

`(1)/(216)` = 0.005 (nearest thousandth)

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=(a_2)/(a_1)=(36)/(216)=\frac16`

`\implies a_n=216 \cdot \frac16^(n-1)`

`\implies a_7=216 \cdot \frac16^(7-1)=(1)/(216)=0.005`