In an AP, if `a = 3.5`, `d = 0` and `n = 101`, then `a_(n)` will be

Options

A. `0`
B. `3.5`
C. `103.5`
D. `104.5`

Explanation

To find the nth term \( a_n \) of an arithmetic progression (AP) where \( a = 3.5 \), \( d = 0 \), and \( n = 101 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the formula for the nth term of an AP**:
The nth term \( a_n \) of an arithmetic progression can be calculated using the formula:
\[ a_n = a + (n - 1) \cdot d \]
where:
- \( a \) is the first term,
- \( d \) is the common difference,
- \( n \) is the term number.

**Hint**: Remember that the formula incorporates the first term and the common difference multiplied by the number of terms minus one.

2. **Substitute the known values into the formula**:
Given:
- \( a = 3.5 \)
- \( d = 0 \)
- \( n = 101 \)

Substitute these values into the formula:
\[ a_n = 3.5 + (101 - 1) \cdot 0 \]

**Hint**: Make sure to perform the subtraction in the parentheses first.

3. **Calculate \( n - 1 \)**:
Calculate \( 101 - 1 \):
\[ 101 - 1 = 100 \]

**Hint**: This step is crucial as it determines how many times the common difference will be added.

4. **Multiply by the common difference \( d \)**:
Now, substitute back into the equation:
\[ a_n = 3.5 + 100 \cdot 0 \]

**Hint**: Remember that multiplying by zero will always yield zero.

5. **Simplify the expression**:
Since \( 100 \cdot 0 = 0 \):
\[ a_n = 3.5 + 0 \]
Therefore:
\[ a_n = 3.5 \]

**Hint**: The final result is simply the first term when the common difference is zero.

### Final Answer:
Thus, the value of \( a_n \) is \( 3.5 \).