Final answer:
The next number in the sequence 10, 37, 82, 145, 226 is found by adding 99, which is the next number in the pattern of differences between consecutive terms that increases by 18 each time, resulting in the next term being 325.
Step-by-step explanation:
The given sequence is 10, 37, 82, 145, 226, and we need to find the next number. To find the pattern, let's inspect the differences between each pair of numbers: 37-10=27, 82-37=45, 145-82=63, 226-145=81. These differences are 27, 45, 63, and 81. We can notice that these numbers themselves form a sequence, where each is 18 more than the previous one (45-27=18, 63-45=18, and 81-63=18). This suggests that the next difference in the original sequence should be 81+18=99.
Given this pattern, to find the next number in the original sequence, we add 99 to the last given number, 226:
226 + 99 = 325
Therefore, the next number in the sequence is 325.