Find the missing number in the series:

$$15, 16.5, 19.5, 24, ?, 37.5$$

Question

Find the missing number in the series:

$$15, 16.5, 19.5, 24, ?, 37.5$$

Accepted Answer

**Solution:**

1. Observe the differences between consecutive terms:
   - $16.5 - 15 = 1.5$
   - $19.5 - 16.5 = 3$
   - $24 - 19.5 = 4.5$

2. The increments are increasing by $1.5$ each time: $1.5, 3, 4.5, ...$

3. Next increment should be $6$ (i.e., $4.5 + 1.5$).

4. So, the missing term is:
   $$24 + 6 = 30$$

5. To verify, the next increment should be $7.5$:
   $$30 + 7.5 = 37.5$$ which matches the given series.

**Answer:** $30$

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