Write the next three numbers of the following sequence. Zero, three, eight, 15, 24.
In order to write the next three terms, we need to find a pattern between the first five terms. To get from zero to three, we add three. To get from three to eight, we add five. To get from eight to 15, we add seven. And to get from 15 to 24, we add nine. The first differences between each of our terms are therefore plus three, plus five, plus seven, and plus nine. We can see that these are consecutive odd numbers.
As odd numbers go up in twos, the second differences are all plus two. This will continue for the whole sequence. To find the first missing number, we need to add 11 to 24. This is equal to 35. We then need to add 13 to 35. This is equal to 48. Finally, we need to add 15 to 48. This is equal to 63. The next three terms of the sequence are 35, 48, and 63.