The number of terms in arithmetics series 7, 11, 15,...,139 is

Options

A. 40
B. 34
C. 30
D. 32

Answer

To find the number of terms in the arithmetic series 7, 11, 15, ..., 139, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the first term (a)**:
The first term of the series is \( a = 7 \).

2. **Identify the common difference (d)**:
The common difference can be calculated as:
\[ d = 11 - 7 = 4 \]

3. **Identify the last term (l)**:
The last term of the series is \( l = 139 \).

4. **Use the formula for the nth term of an arithmetic series**:
The formula for the nth term of an arithmetic series is given by:
\[ a_n = a + (n-1) \cdot d \]
Here, \( a_n \) is the nth term, \( a \) is the first term, \( d \) is the common difference, and \( n \) is the number of terms.

5. **Set up the equation with the last term**:
We know the last term is 139, so we can set up the equation:
\[ 139 = 7 + (n-1) \cdot 4 \]

6. **Simplify the equation**:
Subtract 7 from both sides:
\[ 139 - 7 = (n-1) \cdot 4 \]
\[ 132 = (n-1) \cdot 4 \]

7. **Divide both sides by 4**:
\[ n-1 = \frac{132}{4} \]
\[ n-1 = 33 \]

8. **Solve for n**:
Add 1 to both sides:
\[ n = 33 + 1 = 34 \]

9. **Conclusion**:
The number of terms in the arithmetic series is \( n = 34 \).

### Final Answer:
The number of terms in the arithmetic series is **34**.