Question are based on number/figure series. In each series missing term is mentioned by question mark (?). Find out the missing term in given alternatives and write its alternative number against the correct question number on your answer sheet-
7, 25, 61, 121, ?

Options

A. 230
B. 216
C. 208
D. 211

Answer

To find the missing term in the series 7, 25, 61, 121, ?, we will analyze the pattern in the series step by step.

### Step 1: Identify the pattern
Let's look at the given numbers:
- 7
- 25
- 61
- 121

We can observe that these numbers can be expressed in terms of cubes of integers, with a pattern of subtraction.

### Step 2: Express the numbers in terms of cubes
1. **7** can be expressed as \(2^3 - 1 = 8 - 1\)
2. **25** can be expressed as \(3^3 - 2 = 27 - 2\)
3. **61** can be expressed as \(4^3 - 3 = 64 - 3\)
4. **121** can be expressed as \(5^3 - 4 = 125 - 4\)

### Step 3: Identify the pattern in the cubes and subtractions
From the above, we can see that:
- The first term is \(2^3 - 1\)
- The second term is \(3^3 - 2\)
- The third term is \(4^3 - 3\)
- The fourth term is \(5^3 - 4\)

This suggests that the nth term can be expressed as:
\[ n^3 - (n - 1) \]
where \(n\) is the position in the sequence.

### Step 4: Find the missing term
Now, we need to find the 5th term in the series:
- The 5th term will be \(6^3 - 5\)

Calculating this:
\[ 6^3 = 216 \]
Now subtract 5:
\[ 216 - 5 = 211 \]

Thus, the missing term is **211**.

### Conclusion
The missing term in the series 7, 25, 61, 121, ? is **211**.