Question

Help please with this, ASAP!

Answer 1

Answer:

$a_{n}=12n-8$

Step-by-step explanation:

We have been given a recurrence relation $a_{n+1}=a_{n}+12$ and the first term of the sequence $a_{1}=4$.

We can rewrite the given recurrence relation as: $a_{n+1}-a_{n}=12$

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.

$a_{n}=a_{1}+(n-1)d\\a_{n}=4+(n-1)(12)\\a_{n}=4+12n-12\\a_{n}=12n-8$

This is the required explicit function rule for the given sequence.