contestada

A certain arithmetic sequence has the following explicit formula for the nth term:

an = 2 + (n - 1)(6)

The same sequence has the following recursive formula:

an = an-1 + _____

What number belongs in the blank space in the recursive formula?

Respuesta :

Nirina7
arithmetic sequence general term is an+1 - an =an - an-1= ... = a2 -a1=c
but we have an = 2 + (n - 1)(6) as an expression of the sequence, so c=6
and then an - an -1 =c = 6, from where an = an-1 + 6

Answer:

The nth term for the arithmetic sequence is given by:

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

where,

[tex]a_1[/tex] is the first term

n is the number of terms and

d is the common difference for two consecutive terms.

As per the statement:

A certain arithmetic sequence has the following explicit formula for the nth term:

[tex]a_n = 2+(n-1)(6)[/tex]

⇒[tex]a_1 = 2[/tex] and d = 6

The recursive formula for the arithmetic sequence is given by:

[tex]a_n = a_{n-1}+d[/tex]

Substitute the given values we have;

[tex]a_n = a_{n-1}+6[/tex]

⇒the following recursive formula is, [tex]a_n = a_{n-1}+6[/tex]

Therefore, the number belongs in the blank space in the recursive formula is, 6