Type the missing number in this sequence: 5, 7, _____, 17, 25, 35, 47

Question

Type the missing number in this sequence:  5,    7,    _____,    17,    25,    35,    47

Bytelearn · Accepted Answer

Identify Pattern: 5, 7, _____, 17, 25, 35, 47 Identify the pattern in the sequence. Look at the differences between consecutive terms to see if there is a consistent pattern.Calculate Differences: Calculate the differences between the known consecutive terms. 7 - 5 = 2 17 - 7 = 10 25 - 17 = 8 35 - 25 = 10 47 - 35 = 12 The differences are not consistent, but they seem to be increasing. Let's look for another pattern.Look for Pattern: Look for a pattern in the differences of the differences. 10 - 2 = 8 8 - 10 = -2 10 - 8 = 2 12 - 10 = 2 The differences of the differences are not consistent either. Let's try another approach.Consider Formula Involving Squares or Primes: Consider that the sequence might be based on a formula involving squares or primes. Notice that the numbers are not perfect squares or related to prime numbers in a simple way. Let's try looking at the sequence as a series of increasing gaps.Examine for Increasing Gaps: Examine the sequence again for increasing gaps. 5 to 7 is an increase of 2. 7 to 17 is an increase of 10, which is 2 squared plus 2. 17 to 25 is an increase of 8, which is 2 times 4. 25 to 35 is an increase of 10, which is 2 times 5. 35 to 47 is an increase of 12, which is 2 times 6. It seems that the increases are multiples of 2. Let's see if this pattern holds for the missing number.Determine Increase to 17: Determine the increase needed to go from the missing number to 17. If the pattern of increasing by multiples of 2 holds, the increase before 17 should be 2 times 3, which is 6.Subtract Increase for Missing Number: Subtract the increase from 17 to find the missing number. 17 - 6 = 11 The missing number should be 11 if the pattern of increasing by multiples of 2 holds true.Verify Pattern: Verify the pattern with the newly found number. 5 to 7 is an increase of 2 (2 times 1). 7 to 11 is an increase of 4 (2 times 2). 11 to 17 is an increase of 6 (2 times 3). 17 to 25 is an increase of 8 (2 times 4). 25 to 35 is an increase of 10 (2 times 5). 35 to 47 is an increase of 12 (2 times 6). The pattern holds true, so the missing number is indeed 11.

Type the missing number in this sequence: $\newline$ $5$ , $7$ , $\_$ , $17$ , $25$ , $35$ , $47$

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Type the missing number in this sequence:\newline555, 777, _\__, 171717, 252525, 353535, 474747

Type the missing number in this sequence: $\newline$ $5$ , $7$ , $\_$ , $17$ , $25$ , $35$ , $47$