Find the next number in the series:

$$120, 60, 60, 90, 180, ?$$

Question

Find the next number in the series:

$$120, 60, 60, 90, 180, ?$$

Accepted Answer

**Solution:**

1. Observe the series: $$120, 60, 60, 90, 180, ?$$

2. Look for a pattern in the changes between consecutive terms:
   - From 120 to 60: $$120 	imes \frac{1}{2} = 60$$
   - From 60 to 60: $$60 	imes 1 = 60$$
   - From 60 to 90: $$60 	imes \frac{3}{2} = 90$$
   - From 90 to 180: $$90 	imes 2 = 180$$

3. The multipliers are: $$\frac{1}{2}, 1, \frac{3}{2}, 2$$

4. The pattern in multipliers seems to increase by $$\frac{1}{2}$$ each time.

5. Next multiplier should be $$2 + \frac{1}{2} = \frac{5}{2} = 2.5$$

6. Calculate the next term:
   $$180 	imes 2.5 = 450$$

**Answer:** $450$

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