There are some series given below and each series contains one wrong term. Find out the wrong term from the series:

$$2, 338, 548, 668, 728, 751, 758$$

Question

There are some series given below and each series contains one wrong term. Find out the wrong term from the series:

$$2, 338, 548, 668, 728, 751, 758$$

Accepted Answer

**Solution:**

1. Analyze the series: $$2, 338, 548, 668, 728, 751, 758$$

2. Check the differences between consecutive terms:
   - $338 - 2 = 336$
   - $548 - 338 = 210$
   - $668 - 548 = 120$
   - $728 - 668 = 60$
   - $751 - 728 = 23$
   - $758 - 751 = 7$

3. The differences do not follow a clear pattern initially. Let's check if the terms themselves follow any recognizable pattern.

4. Consider the possibility of the series being related to cubes or squares:
   - $2 = 1^3 + 1$
   - $338$ is close to $7^3 = 343$
   - $548$ is close to $8^3 = 512$
   - $668$ is close to $9^3 = 729$

The terms do not align well with cubes.

5. Another approach is to check if the series is a combination of two interleaved sequences or if the terms are random.

6. Alternatively, check the last three terms:
   - $728$ is $8^3 + 0$ (since $8^3 = 512$, no)
   - $728$ is close to $9^3 - 1 = 728$ (since $9^3 = 729$)

7. Notice $728$ is $9^3 - 1$, $751$ is suspicious because it is not close to any cube or square.

8. Check if $751$ fits the pattern:
   - $751$ is a prime number and does not fit the pattern of cubes or squares.

9. Since $751$ does not fit any recognizable pattern and the other numbers are close to cubes or have some pattern, $751$ is likely the wrong term.

**Answer:** $751$

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