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