Find the wrong number in the following number series?
1750,1750,1743,1717,1654,1529,1315

Options

A. 1750
B. 1743
C. 1529
D. 1717

Answer

To solve the problem of finding the wrong number in the series: 1750, 1750, 1743, 1717, 1654, 1529, 1315, we will follow these steps:

### Step 1: Write down the series
The given series is:
- 1750, 1750, 1743, 1717, 1654, 1529, 1315

### Step 2: Calculate the differences between consecutive numbers
Let's find the differences between each pair of consecutive numbers:
- Difference between 1750 and 1750 = 0
- Difference between 1750 and 1743 = 7
- Difference between 1743 and 1717 = 26
- Difference between 1717 and 1654 = 63
- Difference between 1654 and 1529 = 125
- Difference between 1529 and 1315 = 214

So, the differences are:
- 0, 7, 26, 63, 125, 214

### Step 3: Identify a pattern in the differences
Now, let's analyze the differences:
- The first difference is 0.
- The second difference is 7, which is \(2^3 - 1\) (where \(2^3 = 8\)).
- The third difference is 26, which is \(3^3 - 1\) (where \(3^3 = 27\)).
- The fourth difference is 63, which is \(4^3 - 1\) (where \(4^3 = 64\)).
- The fifth difference is 125, which is \(5^3 - 1\) (where \(5^3 = 126\)).
- The sixth difference is 214, which should be \(6^3 - 1\) (where \(6^3 = 216\)).

### Step 4: Check for discrepancies
From the pattern, we can see that:
- The expected differences should be: 0, 7, 26, 63, 124, 215 (based on the cubes minus one).
- However, we have a difference of 125 instead of 124 and 214 instead of 215.

### Step 5: Identify the wrong number
The difference of 125 indicates that the number before 1529 should have been 1654 - 124 = 1530, not 1529.

Thus, the wrong number in the series is **1529**.

### Final Answer
The wrong number in the series is **1529**.

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