What value will come in place of question mark (?) in number-series given below- 204, 196, 223, 159, 284, ?

Options

A. 126
B. 68
C. 272
D. 142

Answer

To find the value that will replace the question mark (?) in the given number series: 204, 196, 223, 159, 284, ?, we will analyze the pattern in the series step by step.

### Step 1: Identify the pattern
Let's look at the differences between consecutive numbers in the series.

1. From 204 to 196:
\[ 204 - 196 = 8 \]

2. From 196 to 223:
\[ 223 - 196 = 27 \]

3. From 223 to 159:
\[ 223 - 159 = 64 \]

4. From 159 to 284:
\[ 284 - 159 = 125 \]

### Step 2: Recognize the cubes
Now, let's express these differences in terms of cubes:

- \(8 = 2^3\)
- \(27 = 3^3\)
- \(64 = 4^3\)
- \(125 = 5^3\)

### Step 3: Determine the next difference
Following the pattern, the next difference should be \(6^3\):

\[ 6^3 = 216 \]

### Step 4: Calculate the next number
Now, we will add this difference to the last number in the series:

\[ 284 - 216 = 68 \]

### Conclusion
Thus, the value that will come in place of the question mark (?) is **68**.

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