Find out the missing term in the series 0,7,26,63,124,215,`"……….."`

Answer

To find the missing term in the series 0, 7, 26, 63, 124, 215, ..., we can analyze the pattern of the series step by step.

### Step 1: Identify the pattern
The given series is:
0, 7, 26, 63, 124, 215

We can observe that these numbers seem to relate to the cubes of integers. Let's calculate the cubes of the first few integers:

- \(0^3 = 0\)
- \(1^3 = 1\)
- \(2^3 = 8\)
- \(3^3 = 27\)
- \(4^3 = 64\)
- \(5^3 = 125\)
- \(6^3 = 216\)
- \(7^3 = 343\)

### Step 2: Analyze the differences
Now, let's look at how the terms in the series relate to these cubes:

- The first term (0) is \(0^3\).
- The second term (7) can be derived from \(2^3 - 1 = 8 - 1 = 7\).
- The third term (26) can be derived from \(3^3 - 1 = 27 - 1 = 26\).
- The fourth term (63) can be derived from \(4^3 - 1 = 64 - 1 = 63\).
- The fifth term (124) can be derived from \(5^3 - 1 = 125 - 1 = 124\).
- The sixth term (215) can be derived from \(6^3 - 1 = 216 - 1 = 215\).

### Step 3: Find the missing term
Following this pattern, the next term in the series should be derived from \(7^3 - 1\):

- \(7^3 = 343\)
- Therefore, the missing term is \(343 - 1 = 342\).

### Conclusion
The missing term in the series is **342**.

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