What will come in place of question mark (?) in the following series questions?
200,?,236,284,380,572

Options

A. A)228
B. B)208
C. C)224
D. D)212

Answer

To find the missing term in the series: 200, ?, 236, 284, 380, 572, we can follow these steps:

### Step 1: Identify the known terms
The series provided is:
- First term: 200
- Second term: ?
- Third term: 236
- Fourth term: 284
- Fifth term: 380
- Sixth term: 572

### Step 2: Calculate the differences between the known terms
Let's find the differences between the consecutive known terms:
- Difference between 236 and 284:
\( 284 - 236 = 48 \)
- Difference between 284 and 380:
\( 380 - 284 = 96 \)
- Difference between 380 and 572:
\( 572 - 380 = 192 \)

So, we have the differences:
- 48 (from 236 to 284)
- 96 (from 284 to 380)
- 192 (from 380 to 572)

### Step 3: Identify the pattern in the differences
The differences appear to be doubling:
- 48 (which is \( 48 \times 1 \))
- 96 (which is \( 48 \times 2 \))
- 192 (which is \( 48 \times 4 \))

This suggests that the difference before 236 should be half of 48:
- Half of 48 is 24.

### Step 4: Calculate the missing term
Now, we can find the second term (the missing term) by subtracting 24 from 236:
- \( 236 - 24 = 212 \)

### Step 5: Verify the pattern
To verify, we can check:
- From 200 to 212, the difference is:
\( 212 - 200 = 12 \) (which is half of 24)
- From 212 to 236, the difference is:
\( 236 - 212 = 24 \)

This confirms that the pattern holds.

### Conclusion
Thus, the missing term in the series is **212**.