Write a recursive formula and an explicit formula for the following arithmetic sequence. 11, 13, 15, 17, 19, ...
A recursive formula is a = INan=.
(Simplify your answers.)
An explicit formula is an =
(Simplify your answer.)

Please check the explanation.

Step-by-step explanation:

Given the sequence

11, 13, 15, 17, 19, ...

Determining the Recursive formula:

We know that a recursive formula is termed as a formula that specifies each term of the given sequence using the preceding terms.

From the given sequence it is clear that every term can be obtained by adding two to the previous term.

i.e. 13 = 11+2, 15 = 13+2, 17 = 15+2, 19 = 17+2

so

aₙ₊₁ = aₙ+2, for n ≥1

Therefore, a recursive formula is:

Determining the Explicit formula:

Given the sequence

11, 13, 15, 17, 19, ...

An arithmetic sequence has a constant difference 'd' and is defined by  

computing the differences of all the adjacent terms

The difference between all the adjacent terms is the same and equal to

also

so substituting , in the nth terms

Therefore, the Explicit formula is: