Find the missing number in the series:

$$81, 72, 136, 111, ?, 278$$

Question

Find the missing number in the series:

$$81, 72, 136, 111, ?, 278$$

Accepted Answer

**Solution:**

1. Analyze the pattern between consecutive terms:

- From $81$ to $72$: $81 - 9 = 72$ (subtract $3^2$)
- From $72$ to $136$: $72 + 64 = 136$ (add $4^3$)
- From $136$ to $111$: $136 - 25 = 111$ (subtract $5^2$)
- From $111$ to $? $: add $6^3 = 216$ would be too large, so check the original pattern given.

2. Given the original pattern:

- $81 - 3^2 = 72$
- $72 + 4^3 = 72 + 64 = 136$
- $136 - 5^2 = 136 - 25 = 111$
- $111 + 6^3 = 111 + 216 = 327$
- $327 - 7^2 = 327 - 49 = 278$

3. Therefore, the missing number is $327$.

**Answer:** $327$

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