What number should replace the question mark in the following series?

$$1, 1, ?, 15, 105, 945$$

Question

What number should replace the question mark in the following series?

$$1, 1, ?, 15, 105, 945$$

Accepted Answer

**Solution:**

1. Observe the pattern in the series: $$1, 1, ?, 15, 105, 945$$

2. The first term is 1.

3. The second term is also 1, which can be seen as $$1 	imes 1 = 1$$.

4. Let the missing term be *x*. From the pattern, each term after the first is obtained by multiplying the previous term by an odd number increasing by 2 each time:
   - First multiplication: $$1 	imes 1 = 1$$
   - Second multiplication: $$1 	imes 3 = 3$$ (this gives the missing term *x*)
   - Third multiplication: $$3 	imes 5 = 15$$
   - Fourth multiplication: $$15 	imes 7 = 105$$
   - Fifth multiplication: $$105 	imes 9 = 945$$

5. Therefore, the missing term is $$3$$.

**Answer:** $3$

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