Find the missing number in the series:

?. ?, 190, 210, 238, 274, 318

Question

Find the missing number in the series:

?. ?, 190, 210, 238, 274, 318

Accepted Answer

**Solution:**

1. Observe the given series: ?, 190, 210, 238, 274, 318

2. Calculate the differences between consecutive known terms:
   - 210 - 190 = 20
   - 238 - 210 = 28
   - 274 - 238 = 36
   - 318 - 274 = 44

3. The differences are increasing by 8 each time: 20, 28, 36, 44

4. To find the difference before 190, subtract 8 from 20:
   - Previous difference = 20 - 8 = 12

5. Therefore, the missing number before 190 is:
   - 190 - 12 = 178

6. But 178 is not the correct option as per the difference pattern. Let's verify the pattern again carefully.

7. Let's check if the differences are indeed increasing by 8:
   - 210 - 190 = 20
   - 238 - 210 = 28 (20 + 8)
   - 274 - 238 = 36 (28 + 8)
   - 318 - 274 = 44 (36 + 8)

8. So the difference before 190 should be 12 (20 - 8).

9. Hence, the missing number is 190 - 12 = 178.

10. However, 178 is an option but let's check if the series fits better with 186:
    - 186 to 190 = 4
    - 190 to 210 = 20
    - 210 to 238 = 28
    - 238 to 274 = 36
    - 274 to 318 = 44

11. The first difference (186 to 190) is 4, which does not fit the pattern of increasing by 8.

12. Let's try 186 as the missing number and check the differences:
    - 190 - 186 = 4
    - 210 - 190 = 20
    - 238 - 210 = 28
    - 274 - 238 = 36
    - 318 - 274 = 44

13. The differences are 4, 20, 28, 36, 44, which is inconsistent.

14. Now try 170:
    - 190 - 170 = 20
    - 210 - 190 = 20
    - 238 - 210 = 28
    - 274 - 238 = 36
    - 318 - 274 = 44

15. Differences: 20, 20, 28, 36, 44 - no consistent pattern.

16. Try 198:
    - 190 - 198 = -8 (negative, so invalid)

17. So the best fit is 178 with difference 12 before 190.

**Answer:** 178

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