Select the number from among the given options that can replace the question mark (?) in the following series:

9, 5, 6, 10.5, 23, ?

Question

Select the number from among the given options that can replace the question mark (?) in the following series:

9, 5, 6, 10.5, 23, ?

Accepted Answer

**Solution:**

1. Observe the given series: 9, 5, 6, 10.5, 23, ?

2. Analyze the transitions between consecutive terms:
   - From 9 to 5: Multiply by 0.5 and add 0.5
     $$9 	imes 0.5 + 0.5 = 4.5 + 0.5 = 5$$

- From 5 to 6: Add 1
     $$5 + 1 = 6$$

- From 6 to 10.5: Multiply by 1.5 and add 1.5
     $$6 	imes 1.5 + 1.5 = 9 + 1.5 = 10.5$$

- From 10.5 to 23: Multiply by 2 and add 2
     $$10.5 	imes 2 + 2 = 21 + 2 = 23$$

3. Notice the pattern in multipliers and additions:
   - Multipliers: 0.5, 1, 1.5, 2
   - Additions: 0.5, 1, 1.5, 2

4. Following this pattern, the next multiplier and addition should be 2.5 each.

5. Calculate the next term:
   $$23 	imes 2.5 + 2.5 = 57.5 + 2.5 = 60$$

**Answer:** 60

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