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 \( a = 7 \) and the last term \( a_n = 55 \), we can use the formula for the sum of the first \( n \) terms of an AP:

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

### Step-by-Step Solution:

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

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

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

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

5. **Multiply \( \frac{9}{2} \) by \( 62 \)**:
- First, calculate \( \frac{62}{2} = 31 \)
- Then, multiply by \( 9 \):
\[ S_n = 9 \times 31 = 279 \]

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