A series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series:
`45,60,55,?,65,80`

Options

A. `56`
B. `70`
C. `58`
D. `72`

Explanation

To find the missing term in the series `45, 60, 55, ?, 65, 80`, we will analyze the pattern in the series step by step.

### Step 1: Identify the pattern in the series
We start with the given series:
- 45, 60, 55, ?, 65, 80

### Step 2: Calculate the differences between consecutive terms
- From 45 to 60:
\[ 60 - 45 = 15 \]
- From 60 to 55:
\[ 55 - 60 = -5 \]
- From 55 to ?:
\[ ? - 55 = x \quad \text{(we will find this)} \]
- From ? to 65:
\[ 65 - ? = y \quad \text{(we will find this)} \]
- From 65 to 80:
\[ 80 - 65 = 15 \]

### Step 3: Establish the pattern
From the calculations, we can see a pattern emerging:
- The first difference is +15
- The second difference is -5
- The next difference should follow the same pattern, which means we can assume:
- After adding 15, we subtract 5.

### Step 4: Apply the pattern to find the missing term
Following the established pattern:
1. From 55, we add 15:
\[ 55 + 15 = 70 \]
2. Now, we check if we subtract 5 from 70 to get the next term:
\[ 70 - 5 = 65 \]

### Step 5: Conclusion
Since both calculations are consistent with the pattern, the missing term is:
\[ \text{Missing term} = 70 \]

Thus, the correct answer is option **b) 70**.