In the sequence of number 0, 7, 26, 63,…..215, 342 the missing term is

Options

A. A)115
B. B)124
C. C)125
D. D)135

Answer

To find the missing term in the sequence 0, 7, 26, 63, __, 215, 342, we will analyze the pattern of the given numbers step by step.

### Step 1: Identify the sequence
The given sequence is:
0, 7, 26, 63, __, 215, 342

### Step 2: Add 1 to each term
To identify a pattern, we can add 1 to each term in the sequence:
- 0 + 1 = 1
- 7 + 1 = 8
- 26 + 1 = 27
- 63 + 1 = 64
- __ + 1 = __ + 1
- 215 + 1 = 216
- 342 + 1 = 343

This gives us a new sequence:
1, 8, 27, 64, __ + 1, 216, 343

### Step 3: Recognize the cubes
Now, we can identify the pattern in this new sequence:
- 1 = 1³
- 8 = 2³
- 27 = 3³
- 64 = 4³
- __ + 1 = 5³
- 216 = 6³
- 343 = 7³

From this, we can see that the numbers are the cubes of integers starting from 1.

### Step 4: Find the missing term
The missing term corresponds to 5³:
- 5³ = 125

Since we added 1 to each term initially, we need to subtract 1 from 125 to find the original missing term:
- Missing term = 125 - 1 = 124

### Step 5: Conclusion
Thus, the missing term in the original sequence is **124**.