Find the missing term in the following number series:

$$300, \, ?, \, 148, \, 221, \, 441, \, 1101.5$$

Question

Find the missing term in the following number series:

$$300, \, ?, \, 148, \, 221, \, 441, \, 1101.5$$

Accepted Answer

**Solution:**

1. Observe the series: $$300, \, ?, \, 148, \, 221, \, 441, \, 1101.5$$

2. Let's analyze the pattern by checking the relationship between alternate terms.

3. Consider the terms at odd positions: 1st term = 300, 3rd term = 148, 5th term = 441

4. Consider the terms at even positions: 2nd term = ?, 4th term = 221, 6th term = 1101.5

5. Check the ratio or difference between alternate terms:

- From 148 to 441: $441 - 148 = 293$
   - From 221 to 1101.5: $1101.5 - 221 = 880.5$

6. Now, check if the even terms follow a multiplication pattern:

- $221 	imes 5 = 1105$ (close to 1101.5)

7. Check if the odd terms follow a pattern:

- $300 	o 148$ (approximately half minus some value)

8. Try to find the missing 2nd term by assuming the pattern between 1st and 2nd term:

- If the 2nd term is $149$, then the difference between 300 and 149 is $151$.

9. Check if the pattern fits for the rest of the series:

- $149 	imes 1.5 = 223.5$ (close to 221)

- $221 	imes 2 = 442$ (close to 441)

- $441 	imes 2.5 = 1102.5$ (close to 1101.5)

10. The pattern suggests multiplying by increasing factors (1.5, 2, 2.5) starting from the 2nd term.

11. Hence, the missing term is $149$.

**Answer:** $149$

Answer

Answer

Answer

Answer