Question

THIS IS 61 POINTS. Find the first three terms of the sequence described by the following recursive formula: an = 3an – 1 + 2 where a4 = 20

a1=
a2=
a3=

Answer 1

see explanation

Explanation:

Given the recursive formula

`a_(n)` = 3
`a_(n-1)` + 2 and a₄ = 20

Then working in reverse

3a₃ + 2 = 20 ( subtract 2 from both sides )

3a₃ = 18 ( divide both sides by 3 )

a₃ = 6

3a₂ + 2 = 6 ( subtract 2 from both sides )

3a₂ = 4 ( divide both sides by 3 )

a₂ =
`(4)/(3)`

3a₁ + 2 =
`(4)/(3)` ( subtract 2 from both sides )

3a₁ = -
`(2)/(3)` ( divide both sides by 3 )

a₁ = -
`(2)/(9)`

Hence

a₁ = -
`(2)/(9)`

a₂ =
`(4)/(3)`

a₃ = 6

Answer 2

a1 = (-2/9)

a2 = 4/3

a3 = 6

Hope this helps!