Find the missing number in the series
3 23 43 ? 83 103

Options

A. 33
B. 53
C. 63
D. 73

Explanation

To find the missing number in the series 3, 23, 43, ?, 83, 103, we will follow these steps:

### Step 1: Identify the given series
The series is: 3, 23, 43, ?, 83, 103.

### Step 2: Calculate the differences between consecutive terms
We will find the difference between consecutive terms to see if there is a pattern:
- Difference between 23 and 3:
\( 23 - 3 = 20 \)

- Difference between 43 and 23:
\( 43 - 23 = 20 \)

- Difference between 83 and 43 (the missing term):
\( 83 - 63 = 20 \) (assuming the missing term is 63)

- Difference between 103 and 83:
\( 103 - 83 = 20 \)

### Step 3: Analyze the differences
From the calculations, we can see that the difference between each consecutive term is consistently 20.

### Step 4: Establish the pattern
Since the differences are the same (20), we can conclude that this series is an arithmetic progression (AP) with:
- First term (A) = 3
- Common difference (D) = 20

### Step 5: Use the formula for the nth term of an AP
The formula for the nth term of an arithmetic progression is given by:
\[ T_n = A + (n - 1) \times D \]
Where:
- \( T_n \) = nth term
- \( A \) = first term
- \( D \) = common difference
- \( n \) = term number

### Step 6: Find the missing term
We need to find the 4th term (the missing term):
- Here, \( n = 4 \)
- So, substituting the values into the formula:
\[ T_4 = 3 + (4 - 1) \times 20 \]
\[ T_4 = 3 + 3 \times 20 \]
\[ T_4 = 3 + 60 \]
\[ T_4 = 63 \]

### Conclusion
The missing number in the series is **63**.

---