Find the missing term in the following numbers series questons.
2000,?,2164,2308,2504,2760

Options

A. 2049
B. 2036
C. 2064
D. 2100

Answer

To find the missing term in the series: 2000, ?, 2164, 2308, 2504, 2760, we can follow these steps:

### Step 1: Identify the series
The series is:
- 2000, ?, 2164, 2308, 2504, 2760

### Step 2: Calculate the differences between the known terms
Let's calculate the differences between consecutive known terms:
- 2164 - 2308 = 144
- 2308 - 2504 = 196
- 2504 - 2760 = 256

Now, we have the differences:
- 2164 to 2308: 144
- 2308 to 2504: 196
- 2504 to 2760: 256

### Step 3: Analyze the differences
Now let's analyze the differences:
- 144 = 12^2
- 196 = 14^2
- 256 = 16^2

We can see that the differences are perfect squares of even numbers:
- 12^2 (144)
- 14^2 (196)
- 16^2 (256)

### Step 4: Find the missing term's difference
The pattern suggests that the previous difference should be 10^2 (100) since we are moving in increments of 2 in the base of the squares (10, 12, 14, 16).

### Step 5: Calculate the missing term
Now, we can find the missing term by subtracting 100 from 2164:
- 2164 - 100 = 2064

### Step 6: Confirm the missing term
Now we can confirm that the missing term is indeed 2064.

### Final Series:
So the complete series is:
- 2000, 2064, 2164, 2308, 2504, 2760

### Conclusion
The missing term is **2064**.

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