Answer:
[tex]a_5=91[/tex]
Step-by-step explanation:
The general term formula is:
[tex]a_n=2a_{n-1}+5[/tex]
And given first term is "1",
The general term formula means, to get a term, multiply the previous term by 2 and sum it with "5".
Lets find a_2:
[tex]a_2=2a_{1}+5\\a_2=2(1)+5\\a_2=7[/tex]
Now, finding a_3:
[tex]a_3=2a_2+5\\a_3=2(7)+5\\a_3=19[/tex]
Now, a_4:
[tex]a_4=2a_3+5\\a_4=2(19)+5\\a_4=43[/tex]
Finally, finding a_5:
[tex]a_5=2a_4+5\\a_5=2(43)+5\\a_5=91[/tex]
This is the answer.
