Missing Number in the Sequence: 3 14 15 ? 653

To find the missing number in the given sequence, we need to analyze the pattern or rule followed by the numbers. Let's break down the sequence and examine it step by step.

Step 1: Identify the Pattern
Looking at the given sequence, we can observe the following:
- The first number, 3, does not appear to follow any specific pattern.
- The second number, 14, is obtained by squaring the first number and then adding 5 (3^2 + 5 = 9 + 5 = 14).
- The third number, 15, is obtained by adding 1 to the square of the second number (14^2 + 1 = 196 + 1 = 197).

Step 2: Apply the Pattern
Based on the pattern observed, we can deduce that the missing number can be found by adding 1 to the square of the previous number. Let's calculate it:

- The square of the third number, 15, is 225 (15^2 = 225).
- Adding 1 to 225 gives us the missing number, which is 226.

Therefore, the missing number in the sequence 3 14 15 ? 653 is 226.

Step 3: Verify the Answer
We can double-check our answer by applying the pattern to the next number in the sequence:
- The square of 15 is 225.
- Adding 1 to 225 gives us 226, which matches our missing number.

Thus, our answer of 226 is consistent with the pattern observed in the given sequence.

Conclusion
By analyzing the pattern in the given sequence, we determined that the missing number is 226. The pattern involves squaring the previous number and adding 1 to it. This conclusion was verified by applying the pattern to the next number in the sequence.