What is the next number in following?
10, 17, 36, 73, 134, ?

Question

What is the next number in following? 
10, 17, 36, 73, 134, ?

Accepted Answer

To determine the next number in the sequence 10, 17, 36, 73, 134, we need to identify the pattern or rule governing the progression of numbers. Let's analyze the differences between consecutive terms:

1. Difference between 17 and 10: 17 - 10 = 7
2. Difference between 36 and 17: 36 - 17 = 19
3. Difference between 73 and 36: 73 - 36 = 37
4. Difference between 134 and 73: 134 - 73 = 61

Now, let's examine the differences between these differences:

1. Difference between 19 and 7: 19 - 7 = 12
2. Difference between 37 and 19: 37 - 19 = 18
3. Difference between 61 and 37: 61 - 37 = 24

We observe that the second-level differences (12, 18, 24) increase by 6 each time. This suggests a quadratic pattern in the sequence. To find the next difference after 61, we add 6 to the last second-level difference:

24 + 6 = 30

Adding this to the last first-level difference:

61 + 30 = 91

Finally, add this to the last number in the sequence to find the next number:

134 + 91 = 225

Therefore, the next number in the sequence is 225, which corresponds to Option 3.

Explanation of why other options are incorrect:

1. Option 1 (125): This number does not fit the pattern established by the differences and second-level differences. The calculated next number is 225, not 125.

2. Option 2 (217): Similarly, 217 does not align with the pattern of differences. The correct calculation leads to 225.

3. Option 4 (117): This number is significantly lower than the expected next number in the sequence. The pattern clearly indicates that the next number should be 225.

In conclusion, the correct answer is Option 3 (225), as it fits the established pattern of differences in the sequence.