Find the wrong term in the following number series question.
5,13,29,61,125,255,509

Options

A. A)125
B. B)509
C. C)13
D. D)255

Answer

To find the wrong term in the number series 5, 13, 29, 61, 125, 255, 509, we will analyze the pattern of the series step by step.

### Step 1: Identify the Terms
The given series is:
- 1st term: 5
- 2nd term: 13
- 3rd term: 29
- 4th term: 61
- 5th term: 125
- 6th term: 255
- 7th term: 509

### Step 2: Calculate the Differences Between Consecutive Terms
Let's find the differences between each pair of consecutive terms:
- 13 - 5 = 8
- 29 - 13 = 16
- 61 - 29 = 32
- 125 - 61 = 64
- 255 - 125 = 130
- 509 - 255 = 254

So, the differences are:
- 8, 16, 32, 64, 130, 254

### Step 3: Identify the Pattern in the Differences
Now, let's analyze the differences:
- The first difference is 8 (which is 2^3)
- The second difference is 16 (which is 2^4)
- The third difference is 32 (which is 2^5)
- The fourth difference is 64 (which is 2^6)

Following this pattern, the next difference should be:
- 128 (which is 2^7)

### Step 4: Calculate the Expected Next Term
If we add 128 to the last correct term before the suspected wrong term (125), we get:
- 125 + 128 = 253

### Step 5: Identify the Wrong Term
However, the next term in the series is given as 255. Since we calculated that the correct term should be 253, we can conclude that:
- The wrong term in the series is 255.

### Conclusion
The wrong term in the series is **255**.

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