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fredd [130]
3 years ago
7

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

Mathematics
2 answers:
Scilla [17]3 years ago
7 0

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

vladimir2022 [97]3 years ago
4 0
<span>arithmetic sequence general term is an+1 - an =an - an-1= ... = a2 -a1=c
but we have </span><span>an = 2 + (n - 1)(6) as an expression of the sequence, so c=6
and then an - an -1 =c = 6, from where </span><span>an = an-1 + 6</span>
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