In the following number series, only one number is incorrect. Identify the wrong number:

4, 12, 30, 68, 148, 304, 622

Question

In the following number series, only one number is incorrect. Identify the wrong number:

4, 12, 30, 68, 148, 304, 622

Accepted Answer

**Solution:**

1. Observe the series: 4, 12, 30, 68, 148, 304, 622

2. Check the pattern by examining the relation between consecutive terms:

- Calculate the difference between terms:
     - 12 - 4 = 8
     - 30 - 12 = 18
     - 68 - 30 = 38
     - 148 - 68 = 80
     - 304 - 148 = 156
     - 622 - 304 = 318

3. The differences are: 8, 18, 38, 80, 156, 318

4. Now, check if these differences follow a pattern:
   - 8 × 2 + 2 = 18
   - 18 × 2 + 2 = 38
   - 38 × 2 + 4 = 80 (does not fit the previous pattern exactly)

5. Alternatively, check if the terms follow a formula like $a_n = 2^n + n^2$ or similar, but it does not fit well.

6. Try to find the correct term at the 5th position (currently 148):

- If the pattern is doubling the previous difference and adding 2, then:
     - From 8 to 18: (8 × 2) + 2 = 18 (correct)
     - From 18 to 38: (18 × 2) + 2 = 38 (correct)
     - From 38 to next difference: (38 × 2) + 2 = 78 (expected difference)

7. So, the difference after 38 should be 78, but the actual difference is 80.

8. Using 78 as the difference:
   - Next term = 68 + 78 = 146 (instead of 148)

9. Therefore, the wrong number in the series is 148, which should be 146 to maintain the pattern.

**Answer:** 148

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