Find the next number in the series:

7, 4.5, 5.5, 12, 49, ?

Question

Find the next number in the series:

7, 4.5, 5.5, 12, 49, ?

Accepted Answer

**Solution:**

1. Given series: 7, 4.5, 5.5, 12, 49, ?

2. Analyze the pattern between consecutive terms:

- From 7 to 4.5:
     $$7 	imes 0.5 + 1 = 3.5 + 1 = 4.5$$

- From 4.5 to 5.5:
     $$4.5 	imes 1 + 1 = 4.5 + 1 = 5.5$$

- From 5.5 to 12:
     $$5.5 	imes 2 + 1 = 11 + 1 = 12$$

- From 12 to 49:
     $$12 	imes 4 + 1 = 48 + 1 = 49$$

3. The multiplier is doubling each time: 0.5, 1, 2, 4, and next should be 8.

4. From 49 to next term:
   $$49 	imes 8 + 1 = 392 + 1 = 393$$

**Answer:** 393

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