In an A.P. if a = – 7.2, d = 3.6, `a_n` = 7.2, then find the value of n.

Answer

To find the value of n in the given arithmetic progression (A.P.), we can follow these steps:

### Step 1: Write down the formula for the nth term of an A.P.
The nth term of an A.P. can be expressed using the formula:
\[ a_n = a + (n - 1) \cdot d \]
where:
- \( a_n \) is the nth term,
- \( a \) is the first term,
- \( d \) is the common difference,
- \( n \) is the term number.

### Step 2: Substitute the known values into the formula.
We know:
- \( a = -7.2 \)
- \( d = 3.6 \)
- \( a_n = 7.2 \)

Substituting these values into the formula gives:
\[ 7.2 = -7.2 + (n - 1) \cdot 3.6 \]

### Step 3: Simplify the equation.
First, we can isolate the term involving n:
\[ 7.2 + 7.2 = (n - 1) \cdot 3.6 \]
\[ 14.4 = (n - 1) \cdot 3.6 \]

### Step 4: Solve for \( n - 1 \).
Now, divide both sides by 3.6:
\[ n - 1 = \frac{14.4}{3.6} \]
Calculating the right side:
\[ n - 1 = 4 \]

### Step 5: Solve for n.
Finally, add 1 to both sides to find n:
\[ n = 4 + 1 \]
\[ n = 5 \]

### Conclusion:
The value of \( n \) is 5.

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