Find the wrong number in the series given below:
5 17 45 89 161 265

Options

A. 17
B. 45
C. 89
D. 161

Answer

To find the wrong number in the series: 5, 17, 45, 89, 161, 265, we will analyze the pattern in the series step by step.

**Step 1: Identify the pattern in the series.**
We will look for a formula that generates the numbers in the series. The hint is to check if each number can be expressed as a sum of a cube and a square.

**Step 2: Calculate the first number (5).**
1's cube + 2's square:
- \(1^3 + 2^2 = 1 + 4 = 5\)

**Step 3: Calculate the second number (17).**
2's cube + 3's square:
- \(2^3 + 3^2 = 8 + 9 = 17\)

**Step 4: Calculate the third number (45).**
3's cube + 4's square:
- \(3^3 + 4^2 = 27 + 16 = 43\)

**Step 5: Calculate the fourth number (89).**
4's cube + 5's square:
- \(4^3 + 5^2 = 64 + 25 = 89\)

**Step 6: Calculate the fifth number (161).**
5's cube + 6's square:
- \(5^3 + 6^2 = 125 + 36 = 161\)

**Step 7: Calculate the sixth number (265).**
6's cube + 7's square:
- \(6^3 + 7^2 = 216 + 49 = 265\)

**Step 8: Compare the calculated numbers with the series.**
- The series is: 5, 17, 45, 89, 161, 265
- The calculated values are: 5, 17, 43, 89, 161, 265

**Step 9: Identify the wrong number.**
The third number in the series is 45, but we calculated it to be 43. Therefore, the wrong number in the series is **45**.

**Final Answer: The wrong number is 45.**

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