Question

I don't quite get this

Answer 1

The third number is 14.

Explanation:

Step Number

1 -2

2

3 ?

4

5 26

We will assume that this is a linear progression. We can either look for a constant increment between steps, or develop a line equation. We'll do both.

see the attached worksheet.

Constant Increment

The difference in the first and last numbers is (26 - 2) = 24, taken in 4 steps. That is a change of 6/step. The second column of the attachment starts with 2 and adds 6 for each step. It arrives at 26 at step 5, meeting all requirements. The 3rd number is 14 with this approach.

Find Equation

We can also develop an equation for a line connecting all the points. We'll look for one with the form y = mx + b, where m is the slope and b is the y-intercept (the value of y when x is zero).

m, the slope, is calculated as the Rise/Run between the two given points. The Rise is (26 - 2) or 24. The Run is (5 - 1( or 4. The slope (Rise/Run) is 24/4 or 6.

The equation becomes y = 6x + b.

To find b, enter one of the 2 known points and solve for b:

y = 6x + b

2 = 6*1 + b for (1,2)

b = -4

The equation becomes y = 6x - 4

The third column contains the values produced by this equation. They match the approach from above.

The third number is 14.

Answer 2

Answer: 12

1. Let’s check the sequence, by writing every natural number:

For difference by 2:
-2, 0, 2, 4, 6 and (6 < 26)

For difference by 4:
-2, 2, 6, 10, 14 (14 < 26)

For difference by 6:
-2, 4, 10, 16, 22 (22 < 26)

Answer: We see for every 2 number difference, last number increases by 8, and 22 is 4 less than 26, so the wanted number will be 1 bigger than 6:

For 7:
-2, 5, 12, 19, 26

So the third number will be 12.