The first and the last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, then how terms are there in the A.P. ?

Answer

To find the number of terms in the Arithmetic Progression (A.P.) where the first term (a) is 17, the last term (a_n) is 350, and the common difference (d) is 9, we can use the formula for the nth term of an A.P.:

\[ a_n = a + (n - 1) \cdot d \]

### Step-by-Step Solution:

1. **Identify the given values**:
- First term (a) = 17
- Last term (a_n) = 350
- Common difference (d) = 9

2. **Substitute the values into the nth term formula**:
\[ 350 = 17 + (n - 1) \cdot 9 \]

3. **Simplify the equation**:
- First, subtract 17 from both sides:
\[ 350 - 17 = (n - 1) \cdot 9 \]
\[ 333 = (n - 1) \cdot 9 \]

4. **Divide both sides by 9**:
\[ n - 1 = \frac{333}{9} \]
\[ n - 1 = 37 \]

5. **Solve for n**:
- Add 1 to both sides:
\[ n = 37 + 1 \]
\[ n = 38 \]

### Conclusion:
There are **38 terms** in the A.P.