Question

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

I think it would be these
1. -2/9
2. 4/3
3. 6

Answer 2

a1= -2/9

a2= 4/3

a3= 6

Explanation:

`a_n = 3a_(n - 1) + 2`

a_4= 20

lets plug in 4 for n

`a_4 = 3a_(4 - 1) + 2`

`20= 3a_3+ 2`

Subtract 2 from both sides and then divide by 3

18 = 3a_3

`6=a_3`

lets plug in 3 for n and use a3=6 to find a2

`a_3 = 3a_(3 - 1) + 2`

`6= 3a_2+ 2`

Subtract 2 from both sides and then divide by 3

4 = 3a_2

`(4)/(3)=a_2`

lets plug in 2 for n and find out a1

`a_2 = 3a_(2 - 1) + 2`

`(4)/(3)= 3a_1+ 2`

Subtract 2 from both sides and then divide by 3

`(-2)/(3)= 3a_1`

`(-2)/(9)=a_1`