Question

Acellus

Find the fifth term in the sequence
that is defined as follows:
a1 = 1
an = 3an-1 + 2

Answer 1

161

Explanation:

Given:

`a_1=1\\ \\a_n=3a_(n-1)+2`

Find:
`a_5`

First, find the second term. Substitute n=2:

`a_2=3a_1+2=3\cdot 1+2=3+2=5`

Now, find the third term, substitute n=3:

`a_3=3a_2+2=3\cdot 5+2=15+2=17`

Find the 4th term, substitute n=4:

`a_4=3a_3+2=3\cdot 17+2=51+2=53`

At last, find the fifth term, substitute n=5:

`a_5=3a_4+2=3\cdot 53+2=159+2=161`