The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 is

Options

A. 81
B. 64
C. 49
D. 36

Answer

To find the sum of the successive odd numbers 1, 3, 5, 7, 9, 11, 13, and 15, we can use a formula that simplifies the process. Here’s a step-by-step solution:

### Step 1: Identify the odd numbers
The odd numbers given in the question are:
1, 3, 5, 7, 9, 11, 13, 15.

### Step 2: Count the number of odd numbers (n)
We need to determine how many odd numbers are there in the list.
- Counting them: 1, 3, 5, 7, 9, 11, 13, 15 gives us a total of 8 odd numbers.
- So, n = 8.

### Step 3: Use the formula for the sum of consecutive odd numbers
The formula for the sum of the first n consecutive odd numbers is:
\[ \text{Sum} = n^2 \]
Where n is the number of odd numbers.

### Step 4: Substitute the value of n into the formula
Now, substituting n = 8 into the formula:
\[ \text{Sum} = 8^2 = 64 \]

### Step 5: Conclusion
Thus, the sum of the successive odd numbers 1, 3, 5, 7, 9, 11, 13, and 15 is:
\[ \text{Sum} = 64 \]

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