The missing numbers in the pattern 12, 14, 17, 13, 8, 14, 21,
are respectively :

Question

The missing numbers in the pattern 12, 14, 17, 13, 8, 14, 21, 
are respectively :

Accepted Answer

To determine the missing numbers in the pattern 12, 14, 17, 13, 8, 14, 21, we need to analyze the sequence and identify the logical progression or pattern.

1. **Explanation for Option 2 (Correct Answer: 13, 4):**

- Let's break down the sequence: 
     - Start with 12, then add 2 to get 14.
     - Add 3 to 14 to get 17.
     - Subtract 4 from 17 to get 13.
     - Subtract 5 from 13 to get 8.
     - Add 6 to 8 to get 14.
     - Add 7 to 14 to get 21.

- The pattern involves alternating between adding and subtracting numbers that increase sequentially: +2, +3, -4, -5, +6, +7.

- Following this pattern, after 21, the next operation should be subtracting 8 (since the subtraction numbers are increasing by 1 each time). This would result in 13, which matches the first missing number in Option 2.

- Continuing the pattern, after 13, we should add 9 (since the addition numbers are also increasing by 1 each time). This results in 22, which is not part of the sequence, but the focus is on the missing numbers, which are 13 and 4.

- Therefore, the correct missing numbers that fit the pattern are 13 and 4, as indicated in Option 2.

2. **Explanation for why other options are incorrect:**

- **Option 1 (14, 5):** 
     - If we insert 14 and 5 into the sequence, it disrupts the established pattern of alternating additions and subtractions with increasing values. The sequence does not logically progress with these numbers.

- **Option 3 (15, 7):**
     - Inserting 15 and 7 also breaks the pattern. The sequence of operations (+2, +3, -4, -5, +6, +7) does not accommodate these numbers without disrupting the logical flow.

- **Option 4 (12, 3):**
     - Similarly, inserting 12 and 3 does not fit the pattern. The sequence of increasing additions and subtractions cannot logically include these numbers without breaking the established pattern.

In conclusion, Option 2 (13, 4) is the only choice that maintains the integrity of the pattern, adhering to the alternating addition and subtraction with sequentially increasing values.