Question

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

Answer 1

Answer: 10,077,696

Step-by-step explanation: U7=216(6)^6

Un=U1(r)^(n-1)

n=7

r=6

n is your nth term

r is your common ratio

Answer 2

a₇ =
`(1)/(216)`

Explanation:

there is a common ratio between consecutive terms , that is

`(a_(2) )/(a_(1) )` =
`(36)/(216)` =
`(1)/(6)`

`(a_(3) )/(a_(2) )` =
`(6)/(36)` =
`(1)/(6)`

this indicates the sequence is geometric with nth term

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

here a₁ = 216 and r =
`(1)/(6)` , then

a₇ = 216 ×
`((1)/(6)) ^(6)` = 6³ ×
`(1)/(6^6)` = 6³ ×
`6^(-6)` =
`6^(-3)` =
`(1)/(6^3)` =
`(1)/(216)`