What will be the average of first 20 odd numbers ?

Options

A. 19
B. 22
C. 20
D. 12

Answer

To find the average of the first 20 odd numbers, we can follow these steps:

### Step 1: Identify the first 20 odd numbers
The first 20 odd numbers are:
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39.

### Step 2: Find the last odd number
The last odd number in this sequence is 39.

### Step 3: Use the formula for the nth term of an arithmetic progression (AP)
The nth term of an AP can be calculated using the formula:
\[ A_n = A + (n - 1) \cdot d \]
Where:
- \( A \) is the first term (1 in this case),
- \( n \) is the number of terms (20),
- \( d \) is the common difference (2 for odd numbers).

Substituting the values:
\[ A_{20} = 1 + (20 - 1) \cdot 2 \]
\[ A_{20} = 1 + 19 \cdot 2 \]
\[ A_{20} = 1 + 38 = 39 \]

### Step 4: Calculate the average
The average of an arithmetic series can be calculated using the formula:
\[ \text{Average} = \frac{\text{First term} + \text{Last term}}{2} \]
Substituting the first term (1) and the last term (39):
\[ \text{Average} = \frac{1 + 39}{2} \]
\[ \text{Average} = \frac{40}{2} = 20 \]

### Conclusion
The average of the first 20 odd numbers is **20**.

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