Question

Find the 8th term of the geometric sequence 7,−21,63,

Answer 1

a₈ = - 15309

Explanation:

The nth term of a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

Here a₁ = 7 and r =
`(a_(2) )/(a_(1) )` =
`(-21)/(7)` = - 3 , then

a₈ = 7 ×
`(-3)^(7)` = 7 × - 2187 = - 15309

Answer 2

8th term is -15309

Explanation:

`{ \boxed{ \bf{u_(n) = a( {r}^(n - 1) ) }}} \\ { \tt{u_(8) = 7( {( - 3)}^(8 - 1)) }} \\ { \tt{u_(8) = 7( - 2187)}} \\ { \tt{u _(8) = - 15309}}`

r is the common difference, r = -21/7 = -3