Question

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

Answer 1

Answer:

The nth term for the arithmetic sequence is given by:

$a_n = a_1+(n-1)d$

where,

$a_1$ 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:

$a_n = 2+(n-1)(6)$

⇒$a_1 = 2$ and d = 6

The recursive formula for the arithmetic sequence is given by:

$a_n = a_{n-1}+d$

Substitute the given values we have;

$a_n = a_{n-1}+6$

⇒the following recursive formula is, $a_n = a_{n-1}+6$

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

Answer 2

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