The first and last terms of an A.P. are 1 and 7 . If
the sum of its terms is 36 , then the number of
terms will be

Options

A. 6
B. 7
C. 8
D. 9

Answer

To solve the problem, we need to find the number of terms in an arithmetic progression (A.P.) where the first term (a) is 1, the last term (l) is 7, and the sum of the terms (S) is 36.

### Step-by-Step Solution:

1. **Identify the given values:**
- First term (a) = 1
- Last term (l) = 7
- Sum of the terms (S) = 36

2. **Use the formula for the sum of an A.P.:**
The formula for the sum of the first n terms of an A.P. is given by:
\[ S = \frac{n}{2} \times (a + l) \]
where:
- S is the sum of the terms,
- n is the number of terms,
- a is the first term,
- l is the last term.

3. **Substitute the known values into the formula:**
\[ 36 = \frac{n}{2} \times (1 + 7) \]
Simplifying the expression inside the parentheses:
\[ 1 + 7 = 8 \]
Now the equation becomes:
\[ 36 = \frac{n}{2} \times 8 \]

4. **Simplify the equation:**
Multiply both sides by 2 to eliminate the fraction:
\[ 72 = 8n \]

5. **Solve for n:**
Divide both sides by 8:
\[ n = \frac{72}{8} = 9 \]

6. **Conclusion:**
The number of terms (n) in the A.P. is 9.

### Final Answer:
The number of terms in the A.P. is **9**.