Question

What are the two missing terms in the followingarithmetic sequence-14, ....., ......., 13

Answer 1

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

`13\text{ = -14 +3}\cdot\text{d }`

If we add 14 on both sides,

`3d\text{ = 14+13 = 27}`

If we divide by 3 on both sides, we get

`d\text{ = }(27)/(3)=9`

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.