Identify the incorrect number in the following series:

$$56, 53, 105, 314, 1255, 6274, 37643$$

Question

Identify the incorrect number in the following series:

$$56, 53, 105, 314, 1255, 6274, 37643$$

Accepted Answer

**Solution:**

1. Observe the pattern in the series:
   $$56, 53, 105, 314, 1255, 6274, 37643$$

2. Check the relationship between consecutive terms:
   - From $53$ to $105$: approximately doubled ($53 	imes 2 = 106$)
   - From $105$ to $314$: roughly tripled ($105 	imes 3 = 315$)
   - From $314$ to $1255$: about quadrupled ($314 	imes 4 = 1256$)
   - From $1255$ to $6274$: nearly quintupled ($1255 	imes 5 = 6275$)
   - From $6274$ to $37643$: approximately sextupled ($6274 	imes 6 = 37644$)

3. The pattern suggests that starting from the second term, each term is multiplied by an increasing integer (2, 3, 4, 5, 6) to get the next term.

4. However, the first term $56$ does not fit this pattern because $56 	imes 1$ should be $53$ (the second term), which is incorrect.

5. If we replace $56$ with $53$, the series would start as $53, 53, 105, 314, \ldots$, which still doesn't fit perfectly, but the given pattern from the second term onward is consistent.

6. Therefore, the incorrect number in the series is the first term, **56**.

**Answer:** $56$

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