Recall that an arithmetic sequence is obtained by adding the same number to a fixed one. For example consider the arithmetic sequence
1, 3, 5, 7,....
Note that 3 = 1 + 2, 5 = 1 +2*2, 7 = 1 + 3*2.
So, in general, you take the first number and then multiply the constant difference d by the space you want in the sequence. In our example, 5 is two places aways from one, and d=2, so we multiply d by 2 and add it to 1.
Let's take -14 as the first number.
So, the first number (that we don't know) is -14+d. The second missing number is -14+2*d. Finally, we get that 13 = -14+3*d. Using this equation we will find the value of d so we can find the other two numbers.
We have the equation
[tex]13\text{ = -14 +3}\cdot\text{d }[/tex]If we add 14 on both sides,
[tex]3d\text{ = 14+13 = 27}[/tex]If we divide by 3 on both sides, we get
[tex]d\text{ = }\frac{27}{3}=9[/tex]So in our sequence, we get the number by taking the previous number and adding 5. Based on this, the first missing number is
-14 + 9 = -5.
The second missing number is obtaind by taking the previous number and adding 9. So the second missing number is -5 + 9 = 4.
So the two missing numbers from the sequence are -5 and 4.
