Question

Which of the following number sequences could be produced by the expression
2x+x^2

Answer 1

The given expression is

`2x+x^2`

So we can write the general rule for the sequence as

`T_x=2x+x^2`

Recall that the domain of a sequence is the set of natural numbers.

Let us plug in some first few natural numbers to generate the sequence.

When
`x=1`, we obtain,

`T_1=2(1)+(1)^2`

`\rightarrow T_1=2+1`

`\rightarrow T_1=3`

When
`x=2`, we obtain,

`T_2=2(2)+(2)^2`

`\rightarrow T_2=4+4`

`\rightarrow T_2=8`

When
`x=3`, we obtain,

`T_3=2(3)+(3)^2`

`T_3=6+9`

`T_3=15`

When
`x=4`, we obtain,

`T_4=2(4)+(4)^2`

`T_4=8+16`

`T_4=24`

Therefore the number sequence produced by the given expression is,

`\boxed{\bold{3, 8, 15, 24.}}`