Question

Choose the correct alternative that will continue the same pattern and fill in the blank spaces. 2, 7, 14, 23, —–, 47

• A. 34
• B. 31
• C. 38
• D. 27
• E. None of these

Hint:

Check the difference between the terms in the sequence. The differences themselves follow a simple arithmetic progression.

Answer 1

The Correct Option is A

1. Write down the sequence:

   2, 7, 14, 23, ___, 47

2. Find the differences between consecutive terms:
   • Difference between 2nd and 1st term: \(7 - 2 = 5\)
   • Difference between 3rd and 2nd term: \(14 - 7 = 7\)
   • Difference between 4th and 3rd term: \(23 - 14 = 9\)
3. Identify the pattern in the differences:

   The differences are 5, 7, 9, ... This is a sequence of consecutive odd numbers, increasing by 2 each time.

4. Determine the next difference in the pattern:

   The next difference should be \(9 + 2 = 11\).

5. Calculate the missing term:

   Add the next difference (11) to the last known term (23):

   \[ \text{Missing Term} = 23 + 11 = 34 \]

6. Verify the pattern continues:

   If the missing term is 34, the next difference should be \(11 + 2 = 13\).

   Check if \(34 + 13\) equals the last term (47):

   \[ 34 + 13 = 47 \]

   The pattern holds.

7. Compare with Options: The calculated missing term is 34.

The correct option is (a) 34.

Answer 2

Given sequence: 2, 7, 14, 23, ?, 47  

Let's find the differences between terms:

• 7 − 2 = 5
• 14 − 7 = 7
• 23 − 14 = 9

The pattern in differences: +2 each time
So, next difference should be 11 → 23 + 11 = 34
Then: 47 − 34 = 13 → which also fits the pattern (difference keeps increasing by 2). 

Correct answer: (a) 34

Answer 3

The numbers form a pattern where the difference between consecutive terms is increasing by 1.
- 7 - 2 = 5
- 14 - 7 = 7
- 23 - 14 = 9
Hence, the next difference should be 11.
- 23 + 11 = 34