Answer:
[tex]a_n = 1 + 5(n-1)[/tex]
$36
Step-by-step explanation:
I think the part that is confusing you is how to read the math syntax.
The part that says "[tex]a_n=1, if\ n=1[/tex]" just means that a=1 is your starting number. The n=1 is the first iteration.
The part that says "[tex]a_{n}=a_{n-1}+5\ , if\ n>1[/tex]" just means that you add 5 to the previous number every iteration.
They want you to find the number at 8th iteration, n=8. So lets work it out.
n=1: a= 1
n=2: a= 1+5 = 6
n=3: a= 6+5 = 11
n=4: a= 11+5 = 16
n=5: a= 16+5 = 21
n=6: a= 21+5 = 26
n=7: a=26+5 = 31
n=8: a= 31+5 = 36
Or you can use the shortcut:
You're always adding by 5 each time and starting with 1, so:
[tex]a_n = 1 + 5(n-1)[/tex]
where n=8 for the 8th round.
[tex]a_n = 1 + 5(8-1) = 36[/tex]
