Answer:
Option B is correct
3n+4[/tex]
Step-by-step explanation:
The nth term for the arithmetic sequence is given by:
[tex]a_n = a_1 +(n-1)d[/tex] ....[1]
where,
[tex]a_n[/tex] is the nth position
n is the number of term
[tex]a_1[/tex] is the first term and
d is the common difference.
Given the table:
Position(n) Value of Term([tex]a_n[/tex])
1 7
2 10
3 13
4 16
5 19
6 22
from the given table:
At n = 1 ,
[tex]a_1 = 7[/tex]
At n = 2
[tex]a_2 = 10[/tex]
at n = 3
[tex]a_3 = 13[/tex] and so on
Common difference(d) for the sequence is 3
Since,
[tex]d = a_2-a_1=a_3-a_2.....[/tex]
⇒[tex]d = 10-7=13-10......... = 3[/tex]
Substitute d = 3 and [tex]a_1 = 7[/tex] in [1] we have;
[tex]a_n = 7+(n-1)(3)[/tex]
⇒[tex]a_n = 7+3n-3[/tex]
⇒[tex]a_n =3n+4[/tex]
Therefore, the expression gives the number in the nth position in the sequence is, [tex]3n+4[/tex]
