Sita starts to calculate sum of all odd natural numbers less tan 72 . What result does she get ?
A. 1196
B. 1296
C. 1331
D. 1276

Options

A. A
B. B
C. D
D. C

Answer

To find the sum of all odd natural numbers less than 72, we can follow these steps:

### Step 1: Identify the odd natural numbers less than 72
The odd natural numbers less than 72 are:
1, 3, 5, 7, ..., 71

### Step 2: Determine the number of terms (N)
The sequence of odd numbers can be expressed as:
- First term (A) = 1
- Last term (L) = 71

The formula for the nth term of an arithmetic sequence is:
\[ L = A + (n-1) \cdot d \]
where \( d \) is the common difference (which is 2 for odd numbers).

Setting up the equation:
\[ 71 = 1 + (n-1) \cdot 2 \]
\[ 71 - 1 = (n-1) \cdot 2 \]
\[ 70 = (n-1) \cdot 2 \]
\[ n-1 = 35 \]
\[ n = 36 \]

So, there are 36 odd natural numbers less than 72.

### Step 3: Use the formula for the sum of an arithmetic series
The sum \( S \) of the first \( n \) terms of an arithmetic series can be calculated using the formula:
\[ S = \frac{n}{2} \cdot (A + L) \]

Substituting the values we found:
- \( n = 36 \)
- \( A = 1 \)
- \( L = 71 \)

### Step 4: Calculate the sum
\[ S = \frac{36}{2} \cdot (1 + 71) \]
\[ S = 18 \cdot 72 \]
\[ S = 1296 \]

Thus, the result that Sita gets is **1296**.

### Final Answer:
**B. 1296**