Which term is wrong in the following series ?
8, 13, 21, 32, 47, 63, 83

Question

Which term is wrong in the following series ? 
8, 13, 21, 32, 47, 63, 83

Accepted Answer

To determine which term is incorrect in the series 8, 13, 21, 32, 47, 63, 83, we need to identify the pattern or rule governing the sequence.

1. **Identifying the Pattern:**
   - Let's examine the differences between consecutive terms:
     - 13 - 8 = 5
     - 21 - 13 = 8
     - 32 - 21 = 11
     - 47 - 32 = 15
     - 63 - 47 = 16
     - 83 - 63 = 20

- Observing these differences, we notice that they are not consistent. However, if we look closely, we can see that the differences are increasing by a pattern:
     - 5, 8, 11, 15, 16, 20

- The differences should ideally increase by a consistent pattern. Let's assume the pattern should be increasing by 3:
     - 5, 8, 11, 14, 17, 20

- Based on this pattern, the correct differences should be:
     - 8 + 5 = 13
     - 13 + 8 = 21
     - 21 + 11 = 32
     - 32 + 14 = 46 (instead of 47)
     - 46 + 17 = 63
     - 63 + 20 = 83

2. **Explanation for Option 3 (47):**
   - The term 47 is incorrect because, according to the identified pattern, the term following 32 should be 46, not 47. The difference between 32 and 47 is 15, which does not fit the expected pattern of increasing by 3 from the previous difference of 11.

3. **Explanation for Other Options:**
   - **Option 1 (13):** The term 13 is correct because it follows the initial difference of 5 from 8, which fits the pattern.
   - **Option 2 (32):** The term 32 is correct because it follows the difference of 11 from 21, which fits the pattern.
   - **Option 4 (63):** The term 63 is correct because it follows the corrected difference of 17 from 46 (the corrected term), which fits the pattern.

In conclusion, the term 47 is the incorrect term in the series, as it disrupts the consistent pattern of increasing differences by 3. Therefore, Option 3 is the correct answer.