contestada

A recursive rule for an arithmetic sequence is
[tex]a_{1} = - 3i \: a_{n} = a_{n - 1} + 7[/tex]
What is the explicit rule of this sequence?
Note; The "i" in the equation is supposed to be a ";"

Respuesta :

LammettHash

From the recursive rule, you have

[tex]a_2=a_1+7[/tex]

[tex]a_3=a_2+7=a_1+7(2)[/tex]

[tex]a_4=a_3+7=a_1+7(3)[/tex]

[tex]a_5=a_4+7=a_1+7(4)[/tex]

and so on. The general pattern for the [tex]n[/tex]-th term is adding [tex]n-1[/tex] copies of 7 to [tex]a_1[/tex]:

[tex]a_n=a_1+7(n-1)[/tex]

With [tex]a_1=-3[/tex], the sequence is explicitly given by

[tex]a_n=-3+7(n-1)=7n-10[/tex]

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