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write an explicit formula for the sequence -4, 1, 6, 11,...

an= -4+ 5(n+1)
an= -4+ 5(n-1)
an= -4+ (n-1)
an= -4+ 5n

Respuesta :

irspow
This is an arithmetic sequence because each term is 5 more than the previous term, the defining characteristic of an arithmetic sequence which is called the common difference.  All arithmetic sequences can be expressed as:

a(n)=a+d(n-1), a=1st term, d=common difference, n=term number, in this case a=-4 and d=5 so

a(n)=-4+5(n-1)

By applying formula of general term of an AP we got that  explicit formula for the sequence -4, 1, 6, 11,... is  [tex]a_n=-4+5(n-1)\\[/tex]

What is a sequence ?

A sequence is collection of numbers with a particular pattern.

Here given sequence is

-4,1,6,11...

[tex]a_1=-4\\\\a_2=1\\\\a_3=6\\\\a_4=11\\\\\\a_2-a_1=1+4=5\\\\a_3-a_2=6-1=5\\\\a_4-a_3=11-6=5[/tex]

Hence this is an AP with a=-4  and d=5

So general term of this  AP can be written as

[tex]a_n=a+(n-1)d\\\\a_n=-4+5(n-1)\\[/tex]

By applying formula of general term of an AP we got that  explicit formula for the sequence -4, 1, 6, 11,... is  [tex]a_n=-4+5(n-1)\\[/tex]

To learn more about sequence visit :

https://brainly.com/question/6561461

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