Answer :
[tex]a_n = 4n-1[/tex] is the function describe the arithmetic sequence
Solution:
Given arithmetic sequence is:
3, 7, 11, 15, 19, 23
The nth term of arithmetic sequence is given as:
[tex]a_n = a_1+(n-1)d[/tex]
Where,
n is the nth term
d is the common difference between terms
[tex]a_1[/tex] is the first term of sequence
From given,
3, 7, 11, 15, 19, 23
Common difference, d = 7 - 3 = 4
[tex]a_1=3[/tex]
Substituting the values in formula,
[tex]a_n = 3 + (n-1) \times 4\\\\a_n = 3 + 4n - 4\\\\a_n = 4n-1[/tex]
Where, n is positive integer, [tex]n\geq 1[/tex]
Thus the function that describes the arithmetic sequence is found