Answer:
[tex]a_{n}=12n-8[/tex]
Step-by-step explanation:
We have been given a recurrence relation [tex]a_{n+1}=a_{n}+12[/tex] and the first term of the sequence [tex]a_{1}=4[/tex].
We can rewrite the given recurrence relation as: [tex]a_{n+1}-a_{n}=12[/tex]
We know that if difference between two consecutive terms is always constant, the sequence is called an arithmetic sequence. So we are dealing with an arithmetic sequence with first term as 4 and common difference as 12.
We can therefore, write an explicit formula for nth terms of the sequence as.
[tex]a_{n}=a_{1}+(n-1)d\\a_{n}=4+(n-1)(12)\\a_{n}=4+12n-12\\a_{n}=12n-8\\[/tex]
This is the required explicit function rule for the given sequence.
