Question

Find the 11th term of the geometric sequence 2, comma, minus, 6, comma, 18, comma, point, point, .2,−6,18,

Answer 1

a₁₁ = 118098

Explanation:

the nth term of a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

a₁ is the first term, r the common ratio , n the term number

given the sequence 2 , - 6 , 18

with a₁ = 2 and r =
`(a_(2) )/(a_(1) )` =
`(-6)/(2)` = - 3 and n = 11 , then

a₁₁ = 2
`(-3)^(10)` = 2 × 59049 = 118098