Question

25PTS!!

Find the first three terms of the sequence described by the following recursive formula:
an = 3an – 1 + 2 where a4 = 20
a1 =
a2 =
a3 =

NEED HELP NOW. HOW DO YOU DO RECURSIVE FORMULA???!!!!!!!!!

Answer 1

the answer is
a1 =-2/9
a2 =4/3
a3 =6

Answer 2

The recursive formula is given as:

`a_n = 3a_(n-1)+2` , n is the number of terms

where,

`a_4 = 20`

We have to find first three terms of the sequence.

For n =4 ;

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

⇒
`a_4 = 3a_3+2`

⇒
`20 = 3a_3+2`

Subtract 2 from both sides we have;

`18= 3a_3`

Divide both sides by 3 we have;

`6 = a_3`

or

`a_3 =6`

For n = 3;

`a_ 3= 3a_(2)+2`

⇒
`6 = 3a_2+2`

Subtract 2 from both sides we have;

`4= 3a_2`

Divide both sides by 3 we have;

`a_2 = (4)/(3)`

For n =2

`a_2= 3a_(1)+2`

⇒
`(4)/(3) =3a_1+2`

Subtract 2 from both sides we have;

`-(2)/(3)= 3a_3`

Divide both sides by 3 we have;

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

Therefore, the first three terms of the sequence are:

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

`a_2 = (4)/(3)`

`a_3 =6`