I need the equation for these numbers:

3, 9, 19, 33, 51

I see that the pattern goes up by 6, then 10, then 14, then 18 (4 more each time)

I tried this:

subtract 1 from each .... 2,8,18,32,50
divide each by 2 .... 1,4,9,16,25...
do you recognize these numbers?

mmmh!
now pick a number n, and perform the above steps with their "inverse" operation in reverse order.

thanks

Did you get

number = 2n^2 + 1

To find the equation for the given numbers, we need to identify the pattern and the relationship between the numbers. From the information you provided, it appears that each number is increasing by a certain amount in every step.

To determine this pattern, let's examine the differences between adjacent numbers:

9 - 3 = 6
19 - 9 = 10
33 - 19 = 14
51 - 33 = 18

As you mentioned, the differences between adjacent numbers are increasing by 4 each time: 6, 10, 14, 18.

Now, we have to determine the relationship between these differences and the position of the numbers in the sequence.

Looking at the differences, we can observe that the first difference (6) corresponds to the 2nd number (9), the second difference (10) corresponds to the 3rd number (19), and so on. The relationship seems to be that the difference is equal to 4 multiplied by the position of the number minus 1.

Using this information, we can create an equation to generate the numbers in the sequence. Let's call the position of the number "n." The equation would be:

Number = 4n + constant

To find the value of the constant, we can substitute one of the numbers and its position into the equation. Let's use the first number (3) and its position (1):

3 = 4 * 1 + constant

Simplifying the equation:

3 = 4 + constant

Subtracting 4 from both sides:

3 - 4 = constant

-1 = constant

Now we have the value of the constant. Plugging it back into the equation:

Number = 4n - 1

Therefore, the equation for the given sequence is:

Number = 4n - 1

Using this equation, you can generate any number in the sequence by substituting the position of the number (n) into the equation.