Find the missing term that can be filled at the "?" place in the series:
1, 3, 7, 22, 67, ?, 1077

Question

Accepted Answer

#### Step 1: Analyze the Series
The given series is: **1, 3, 7, 22, 67, ?, 1077**.

#### Step 2: Calculate Differences Between Consecutive Terms
The differences between consecutive terms are:  
- $$3 - 1 = 2$$  
- $$7 - 3 = 4$$  
- $$22 - 7 = 15$$  
- $$67 - 22 = 45$$  
- $$? - 67 = 	ext{unknown}$$  
- $$1077 - ? = 	ext{unknown}$$

#### Step 3: Analyze the Pattern in Differences
The first-level differences are: **2, 4, 15, 45**.

Now find the second-level differences:  
- $$4 - 2 = 2$$  
- $$15 - 4 = 11$$  
- $$45 - 15 = 30$$

The second-level differences are: **2, 11, and 30**. This suggests a pattern of increasing differences.

#### Step 4: Predict the Next Difference
The next second-level difference follows the pattern of approximately tripling:  
- $$30 	imes \approx3 = 	ext{~90}$$

Add this to the last first-level difference (45):  
- Next first-level difference = $$45 + 	ext{90} = 	ext{135}$$.

#### Step 5: Calculate the Missing Term
Add this predicted difference to the last known term (67):  
- Missing term = $$67 + 	ext{135} = 	ext{267}$$.

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Thus, the missing term is **267**, making Option **(d)** correct.

Answer

Answer

Answer