Question

{-2, 6, -18, 54.-162,...}
Can anyone please find the explicit rule and 10th term please.

Answer 1

see explanation

Explanation:

There is a common ratio between consecutive terms , that is

6 ÷ - 2 = - 18 ÷ 6 = 54 ÷ - 18 = - 162 ÷ 54 = - 3

This indicates the sequence is geometric with explicit rule

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

Here a₁ = - 2 and r = - 3 , then

a₁₀ = - 2
`(-3)^(9)` = - 2 × - 19683 = 39366

Answer 2

10th number is: 39366

Example of sequence:

(common ratio is found by [6/-2], [-18/6] which both give -3)