Solving the Number Series: 7, 14, 11, 22, 17, 34, ?

To complete the given number series, we need to identify the underlying pattern or logic connecting the numbers. Let's examine the relationship between consecutive terms:

• The first term is 7.
• The second term is 14. The operation from 7 to 14 is multiplication by 2: 
  \(7 \times 2 = 14\)
• The third term is 11. The operation from 14 to 11 is subtraction of 3: 
  \(14 - 3 = 11\)
• The fourth term is 22. The operation from 11 to 22 is multiplication by 2: 
  \(11 \times 2 = 22\)
• The fifth term is 17. The operation from 22 to 17 is subtraction of 5: 
  \(22 - 5 = 17\)
• The sixth term is 34. The operation from 17 to 34 is multiplication by 2: 
  \(17 \times 2 = 34\)

Identifying the Pattern

The series follows an alternating pattern of two operations:

1. Multiplying the current number by 2.
2. Subtracting a number from the current number.

Let's look at the numbers being subtracted: 3, 5. This sequence consists of consecutive odd numbers, increasing by 2 each time.

Determining the Next Term

Following the established pattern:

• The last operation was multiplication by 2 (17 * 2 = 34).
• The next operation should be subtraction.
• The sequence of subtractions is 3, 5. The next odd number in this sequence is 7 (since 5 + 2 = 7).
• Therefore, we subtract 7 from the last term (34): 
  \(34 - 7 = 27\)

Thus, the next number in the series is 27.

Final Answer Verification

The series progresses as follows:

• 7
• \(7 \times 2 = 14\)
• \(14 - 3 = 11\)
• \(11 \times 2 = 22\)
• \(22 - 5 = 17\)
• \(17 \times 2 = 34\)
• \(34 - 7 = 27\)

The number 27 correctly follows the identified pattern.