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que expresiones algebraicas generan la siguiente sucesion 1,4,7,10,13​

Sagot :

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

  • Algebraic expression

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

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