Answer:
Option 2nd is correct
2n
Step-by-step explanation:
The nth term for the arithmetic sequence is given by:
[tex]a_n =a+(n-1)d[/tex] ....[1]
where,
a is the first term
d is the common difference
and n is the number of terms.
As per the statement:
Given the sequence 2, 4, 6, 8, 10, . . .
This is an arithmetic sequence
here, a = 2 and d = 2
Since,
4-2 = 2,
6-4 = 2,
8-6 = 2 and so on...
Substitute the given values in [1] we have.
[tex]a_n = 2+(n-1)(2)[/tex]
⇒[tex]a_n = 2+2n-2[/tex]
Simplify:
[tex]a_n = 2n[/tex]
therefore, the following represents the general term for the sequence is, 2n
