Find the next number in the series:

$$7, 16, 45, 184, 915, ?$$

Question

Find the next number in the series:

$$7, 16, 45, 184, 915, ?$$

Accepted Answer

**Solution:**

1. Observe the series: $$7, 16, 45, 184, 915, ?$$

2. Let's analyze the pattern by checking the relation between consecutive terms.

3. Calculate the ratio or difference:
   - From 7 to 16: $16 = 7 	imes 2 + 2$ (approximate)
   - From 16 to 45: $45 = 16 	imes 2 + 13$ (not consistent)

4. Try to check if each term is generated by multiplying the previous term by an increasing integer and then adding an increasing integer:

- $16 = 7 	imes 2 + 2$
   - $45 = 16 	imes 3 - 3$
   - $184 = 45 	imes 4 + 4$
   - $915 = 184 	imes 5 - 5$

5. The pattern seems to be:
   - Multiply the previous term by $n$ (starting from 2 and increasing by 1 each time)
   - Then add or subtract $n$ alternately

6. Following this pattern, the next term should be:
   - Multiply $915$ by $6$ and add $6$ (since the last operation was subtract 5, now add 6):

$$915 	imes 6 + 6 = 5490 + 6 = 5496$$

**Answer:** $5496$

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