What is the sum of the first 17 terms of an arithmeitc progresion if the first term is -20 and last term is 28

Options

A. 68
B. 156
C. 142
D. 242

Answer

To find the sum of the first 17 terms of an arithmetic progression (AP) where the first term \( a = -20 \) and the last term \( l = 28 \), 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 values:**
- First term \( a = -20 \)
- Last term \( l = 28 \)
- Number of terms \( n = 17 \)

2. **Substitute the values into the formula:**
\[ S_{17} = \frac{17}{2} \times (-20 + 28) \]

3. **Calculate \( -20 + 28 \):**
\[ -20 + 28 = 8 \]

4. **Substitute back into the formula:**
\[ S_{17} = \frac{17}{2} \times 8 \]

5. **Calculate \( \frac{17}{2} \times 8 \):**
\[ S_{17} = \frac{17 \times 8}{2} = \frac{136}{2} = 68 \]

6. **Final Result:**
The sum of the first 17 terms of the arithmetic progression is \( 68 \).