The recursive formula will be g(n) = g(n-1) + 5
What is recursive formula ?
"A recursive formula refers to a formula that defines each term of a sequence using the preceding term(s). The recursive formulas define the following parameters:
The first term of the sequence.
The pattern rule to get any term from its previous term.
Recursive Formula for Arithmetic Sequence
The recursive formula to find the nth term of an arithmetic sequence is:
an = an-1 + d for n ≥ 2
where
an is the nth term of a A.P.
d is the common difference."
Given,
[tex]g(n) = 1 + 5(n-1)[/tex]
Let the remaining term be x
Now,
[tex]g(n) = g(n-1) + x 1 + 5(n-1) = 1 + 5(n - 1 - 1) + x\\\\ 1 + 5n - 5 = 1 + 5n - 10 + x \\\\x = 5[/tex]
So, [tex]g(n) = g(n-1) + 5[/tex]
And, [tex]g(1) = 1 + 5(1 - 1) + 5[/tex]
[tex]g(1) = 6[/tex]
Hence, [tex]g(1) = 6[/tex] and [tex]g(n) = g(n-1) + 5[/tex]
To know more about recursive formula here
https://brainly.com/question/8972906
#SPJ3
