To find the next number in the given series [tex]\(10, 17, 26, 37\)[/tex], let's follow these steps:
1. Identify the differences between the consecutive terms:
- The difference between the second term (17) and the first term (10) is [tex]\(17 - 10 = 7\)[/tex].
- The difference between the third term (26) and the second term (17) is [tex]\(26 - 17 = 9\)[/tex].
- The difference between the fourth term (37) and the third term (26) is [tex]\(37 - 26 = 11\)[/tex].
2. Examine the pattern in the differences:
- The first difference is [tex]\(7\)[/tex].
- The second difference is [tex]\(9\)[/tex].
- The third difference is [tex]\(11\)[/tex].
We can observe that the differences between consecutive terms are increasing by 2.
3. Predict the next difference:
- Since the differences increase by 2 each time, the next difference will be [tex]\(11 + 2 = 13\)[/tex].
4. Calculate the next number in the series:
- The last number in the series is [tex]\(37\)[/tex].
- Adding the next difference to the last number: [tex]\(37 + 13 = 50\)[/tex].
Therefore, the next number in the series is [tex]\(50\)[/tex].
The correct choice is:
C. 50
