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

Answer:

see explanation

Step-by-step 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 = $\frac{4}{3}$

3a₁ + 2 = $\frac{4}{3}$ ( subtract 2 from both sides )

3a₁ = - $\frac{2}{3}$ ( divide both sides by 3 )

a₁ = - $\frac{2}{9}$

Hence

a₁ = - $\frac{2}{9}$

a₂ = $\frac{4}{3}$

a₃ = 6

Answer 2

a1 = (-2/9)

a2 = 4/3

a3 = 6

Hope this helps!