What will come in place of (?) in the following number series?
72,80,71,135,?,326

Options

A. 125
B. 110
C. 90
D. 105

Answer

To solve the number series problem, we will analyze the given series step by step.

**Given Series:** 72, 80, 71, 135, ?, 326

### Step 1: Identify the pattern in the series
We will look for a pattern by examining the differences between consecutive terms.

1. From 72 to 80:
- **Difference:** 80 - 72 = 8
2. From 80 to 71:
- **Difference:** 71 - 80 = -9
3. From 71 to 135:
- **Difference:** 135 - 71 = 64
4. From 135 to the unknown term (let's call it x):
- We need to find the difference here.
5. From the unknown term (x) to 326:
- **Difference:** 326 - x

### Step 2: Analyze the differences
Now, we can summarize the differences we have calculated:
- The differences are: +8, -9, +64, ?, ?

### Step 3: Identify the pattern in the differences
Looking at the differences:
- The first difference is +8 (which is 2^3).
- The second difference is -9 (which is -3^2).
- The third difference is +64 (which is 4^3).

Following this pattern, we can see that the differences alternate between cubes and squares:
- 2^3, -3^2, 4^3, ?, ?

### Step 4: Determine the next difference
Continuing the pattern:
- The next difference should be -5^2 = -25.

### Step 5: Calculate the unknown term
Now we can calculate the unknown term (x):
- From 135, we subtract 25:
- x = 135 - 25 = 110.

### Step 6: Verify the next term
Now, we need to check the difference from 110 to 326:
- The next difference should be +6^3 = 216.
- So, 110 + 216 = 326, which confirms our calculations.

### Conclusion
The missing term in the series is **110**.

### Final Answer
The answer is **110**.

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