Answer:
161
Step-by-step explanation:
Given:
[tex]a_1=1\\ \\a_n=3a_{n-1}+2[/tex]
Find: [tex]a_5[/tex]
First, find the second term. Substitute n=2:
[tex]a_2=3a_1+2=3\cdot 1+2=3+2=5[/tex]
Now, find the third term, substitute n=3:
[tex]a_3=3a_2+2=3\cdot 5+2=15+2=17[/tex]
Find the 4th term, substitute n=4:
[tex]a_4=3a_3+2=3\cdot 17+2=51+2=53[/tex]
At last, find the fifth term, substitute n=5:
[tex]a_5=3a_4+2=3\cdot 53+2=159+2=161[/tex]
