Find the next number in the series:

3, 5, 15, 45, 113, ?

Question

Find the next number in the series:

3, 5, 15, 45, 113, ?

Accepted Answer

**Solution:**

1. Given series: 3, 5, 15, 45, 113, ?

2. Calculate the differences between consecutive terms:
   - 5 - 3 = 2
   - 15 - 5 = 10
   - 45 - 15 = 30
   - 113 - 45 = 68

3. Check if these differences follow a pattern:
   - 2 = 1³ + 1
   - 10 = 2³ + 2
   - 30 = 3³ + 3
   - 68 = 4³ + 4

4. Next difference should be:
   - 5³ + 5 = 125 + 5 = 130

5. Therefore, next term = 113 + 130 = 243

**Answer:** 243

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