Type the missing number in this sequence: 5, 7, 11, _____, 25, 35, 47, 61

Question

Type the missing number in this sequence:  5,    7,    11,    _____,    25,    35,    47,    61

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Identify Pattern: 5, 7, 11, _____, 25, 35, 47, 61 Identify the pattern in the sequence. We need to observe the differences between consecutive terms to see if there is a consistent pattern.Calculate Differences: Calculate the differences between consecutive terms that are given. 7 - 5 = 2 11 - 7 = 4 The differences are not consistent so far, so let's look at the next set of differences. 25 - 11 = 14 35 - 25 = 10 47 - 35 = 12 61 - 47 = 14 The differences are not consistent, but they are increasing. We need to find the pattern in the differences.Look for Patterns: Look for a pattern in the differences of the differences. 4 - 2 = 2 14 - 4 = 10 10 - 14 = -4 12 - 10 = 2 14 - 12 = 2 It seems that the differences of the differences are not consistent either. We need to look for another pattern.Analyze Numbers: Analyze the sequence of given numbers to identify if they are special numbers, such as prime numbers. 5 is a prime number. 7 is a prime number. 11 is a prime number. 25 is not a prime number, but it is a square number (5^2). 35 is not a prime number (5 * 7). 47 is a prime number. 61 is a prime number. It seems that most of the numbers are prime numbers, except for 25 and 35. Let's see if the missing number is a prime number.Check Prime Numbers: Check the prime numbers between 11 and 25 to find the missing number. The prime numbers between 11 and 25 are 13, 17, 19, and 23. Since 25 is not a prime number, we can assume that the sequence is not strictly prime numbers. However, 25 is the square of 5, and 35 is the product of 5 and 7, which are both prime. Let's see if the missing number is related to prime numbers in a similar way.Analyze Relationships: Analyze the relationship between the non-prime numbers and the prime numbers in the sequence. 25 is 5 squared, and 5 is the prime number before 7. 35 is the product of 5 and 7, which are consecutive prime numbers. The missing number should be related to the prime numbers before and after 11, which are 7 and 13.Calculate Missing Number: Calculate the missing number based on the relationship between the non-prime numbers and the prime numbers. The missing number should be the product of 7 and 13, as 35 is the product of 5 and 7. 7 * 13 = 91Verify Solution: Verify if 91 fits the pattern in the sequence. 91 is not a prime number, but it is the product of two consecutive prime numbers (7 and 13), similar to how 35 is the product of 5 and 7. The sequence seems to be a mix of prime numbers and products of consecutive prime numbers.

Type the missing number in this sequence: $\newline$ $5$ , $7$ , $11$ , $\_$ , $25$ , $35$ , $47$ , $61$

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Type the missing number in this sequence:\newline555, 777, 111111, _\__, 252525, 353535, 474747, 616161

Type the missing number in this sequence: $\newline$ $5$ , $7$ , $11$ , $\_$ , $25$ , $35$ , $47$ , $61$