Which formula can be used to find the nth term of the following geometric sequence? − 2/9 , 2/3 , −2, 6,…

aₙ = (-1)ⁿ2(3)ⁿ⁻³

Step-by-step explanation:

The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

We can get the value for r by dividing aₙ by aₙ₋₁.

a₄/a₃ = 6 ÷ (-2)

a₄/a₃ = -3

r = -3

a₁ = -2/9

aₙ = (-2/9)(-3)ⁿ⁻¹

aₙ = (-2/3²)(-3)ⁿ⁻¹              Factor out the 3s from the 9

aₙ = -2(3²)(-1)ⁿ⁻¹(3)ⁿ⁻¹        Factor -1 from  and -3

aₙ  = (-1)(2)(-1)ⁿ⁻¹(3)ⁿ⁻³      Combine like terms

aₙ = 2(-1)ⁿ⁻²(3)ⁿ⁻³             Multiply the -1 term by (-1)² (=1)

aₙ = (-1)ⁿ2(3)ⁿ⁻³

The (-1)ⁿ term makes the terms alternately positive and negative.

1. 8

2. 9

3. 20

4. 3

5. 17

6. 2.2

7. 11.25

8. 1

9. 14

10. 2

step-by-step explanation:

thats the first half