Question

Which of the following represents the general term for the sequence 2, 4, 6, 8, 10, . . .?

n + 1
2n
2n - 1

Answer 1

Option 2nd is correct

2n

Explanation:

The nth term for the arithmetic sequence is given by:

`a_n =a+(n-1)d` ....[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.

`a_n = 2+(n-1)(2)`

⇒
`a_n = 2+2n-2`

Simplify:

`a_n = 2n`

therefore, the following represents the general term for the sequence is, 2n

Answer 2

The general term for the sequence 2, 4, 6, 8, 10, . . . is 2n.