What is the sum of the first 9 terms of an arithmetic progression if the first term is 7 and the last term is 55

Options

A. 219
B. 137
C. 231
D. 279

Answer

To find the sum of the first 9 terms of an arithmetic progression (AP) where the first term is 7 and the last term is 55, we can use the formula for the sum of the first n terms of an AP:

\[ S_n = \frac{n}{2} \times (a + l) \]

Where:
- \( S_n \) is the sum of the first n terms,
- \( n \) is the number of terms,
- \( a \) is the first term,
- \( l \) is the last term.

### Step-by-Step Solution:

1. **Identify the given values**:
- First term \( a = 7 \)
- Last term \( l = 55 \)
- Number of terms \( n = 9 \)

2. **Substitute the values into the formula**:
\[ S_9 = \frac{9}{2} \times (7 + 55) \]

3. **Calculate the sum inside the parentheses**:
\[ 7 + 55 = 62 \]

4. **Substitute back into the formula**:
\[ S_9 = \frac{9}{2} \times 62 \]

5. **Multiply \( \frac{9}{2} \) by 62**:
\[ S_9 = \frac{9 \times 62}{2} = \frac{558}{2} = 279 \]

6. **Final Result**:
The sum of the first 9 terms of the arithmetic progression is \( S_9 = 279 \).