The arithmetic progression allows to find the algebraic formula of the sequence 1, 4, 7, 10, 13 is:
aₙ = 3n -2
given parameters
- Values of the sequence 1, 4, 7, 10, 13
to find
An arithmetic progression is a sequence of numbers such that the difference between two consecutive numbers is constant.
[tex]a_n - a_{n-1} = d[/tex]
where aₙ and a_{n-1} are two consecutive terms and d is the ratio between them
in this case
d = 4 -1 = 3
d = 7 -4 = 3
d = 10 - 7 = 3
d = 13 -10 = 3
so the ratio of the sequence is 3
the first term of the sequence is given
a₁ = 1
so we can write the general arithmetic progression
[tex]a_n = a_1 + (n-1) d[/tex]
where aₙ is the nth term, a₁ is the first term, d is the ratio and n is an integer that serves as a counter.
We substitute
aₙ = 1 + (n-1) 3
aₙ = 1 + 3n - 3
aₙ = 3n - 2
Using the arithmetic progression we find the algebraic formula of the given sequence is: aₙ = 3n -2
learn more arithmetic progression here: brainly.com/question/12006170
