Answer:
[tex]a_n=20+6(n-1)[/tex]
Step-by-step explanation:
Arithmetic Sequence
The arithmetic sequences are identified because each term is obtained by adding or subtracting a fixed number to the previous term. For example, the sequence 5, 12, 19, 26, 33... is arithmetic because each term is calculated by adding 7 to the previous term. The constant number is called the common difference r. The first term is identified as a1.
We are given a recursive formula for a sequence as follows:
[tex]20, a_{n-1}+6[/tex]
This means the sequence is
20, 26, 32, 38, ...
The common difference is r=6 and the first term is a1=20. The equation to calculate the nth term of an arithmetic sequence is:
[tex]a_n=a_1+(n-1)r[/tex]
Substituting the known values:
[tex]a_n=20+6(n-1)[/tex]
The explicit equation of the arithmetic sequence is
[tex]\boxed{a_n=20+6(n-1)}[/tex]
