Question

¿Cuál serie numérica tiene como regla general Xn = 2n +1?

a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5

Answer 1

The series of numbers that correspond to the general rule of
`X_n=2n+1` is {3, 5, 7, 9}.

Explanation:

We are given with the following series options below;

a. 3, 5, 7, 9

b. 2, 4, 5, 8

c. 4, 6, 8,10

d. 2, 3, 4, 5

And we have to identify what number series has a general rule as
`X_n=2n+1`.

For this, we will put the values of n in the above expression and then will see which series is obtained as a result.

So, the given expression is ;
`X_n=2n+1`

If we put n = 1, then;

`X_1=(2* 1)+1`

`X_1 = 2+1 = 3`

If we put n = 2, then;

`X_2=(2* 2)+1`

`X_2 = 4+1 = 5`

If we put n = 3, then;

`X_3=(2* 3)+1`

`X_3 = 6+1 = 7`

If we put n = 4, then;

`X_4=(2* 4)+1`

`X_4 = 8+1 = 9`

Hence, the series of numbers that correspond to the general rule of
`X_n=2n+1` is {3, 5, 7, 9}.