Question

Which of the following number sequences could be produced by the expression 2x+x2? A. 3, 8, 15, 24 B. 1, 3, 5, 7 C. 1, -1, -3, -5 D. 2, 7, 14, 21

Answer 1

A) 3, 8, 15, 24 is correct.

Letting x be the term number (position in the sequence), for the first term, we have:

2(1) + 1^2 = 2+1 = 3

For the second term:
2(2) + 2^2 = 4+4 = 8

Third term:
2(3) + 3^2 = 6+9 = 15

Fourth term:
2(4) + 4^2 = 8+16 = 24

Answer 2

A.
`3,8,15,24`

Explanation:

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`

`\Rightarrow T_3=6+9`

`\Rightarrow T_3=15`

When
`x=4`, we obtain,

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

`\Rightarrow T_4=8+16`

`\Rightarrow T_424`

Therefore the number sequence produced by the given expression is,

`3,8,15,24`

The correct answer is option A