What will come in place of question mark (?) in the following series questions?
100,180,294,448,648,?

Options

A. A)1040
B. B)1020
C. C)980
D. D)900

Answer

To find the missing term in the series: 100, 180, 294, 448, 648, ?, we can analyze the pattern in the series step by step.

### Step 1: Identify the Pattern
Let's look at the terms one by one:
- The first term is 100.
- The second term is 180.
- The third term is 294.
- The fourth term is 448.
- The fifth term is 648.

### Step 2: Express Each Term in a Formula
We can express each term in terms of a formula:
1. The first term (100) can be expressed as \(5^2 \times (5 - 1) = 25 \times 4 = 100\).
2. The second term (180) can be expressed as \(6^2 \times (6 - 1) = 36 \times 5 = 180\).
3. The third term (294) can be expressed as \(7^2 \times (7 - 1) = 49 \times 6 = 294\).
4. The fourth term (448) can be expressed as \(8^2 \times (8 - 1) = 64 \times 7 = 448\).
5. The fifth term (648) can be expressed as \(9^2 \times (9 - 1) = 81 \times 8 = 648\).

### Step 3: Determine the Next Term
From the pattern, we can see that each term can be represented as:
- \(n^2 \times (n - 1)\), where \(n\) starts from 5 and increases by 1 for each subsequent term.

Following this pattern, the next term (the sixth term) will be:
- \(10^2 \times (10 - 1) = 100 \times 9 = 900\).

### Conclusion
Thus, the missing term in the series is **900**.