In an A.P:
given l = 28 , S= 144 , and there are total 9 terms . Find a .

Answer

To solve the problem step by step, we will use the formula for the sum of the first n terms of an arithmetic progression (A.P.).

### Given:
- Last term (l) = 28
- Sum of n terms (S) = 144
- Total number of terms (n) = 9

### We need to find:
- First term (a)

### Step 1: Write down the formula for the sum of the first n terms of an A.P.
The formula for the sum of the first n terms (S_n) of an A.P. is given by:
\[ S_n = \frac{n}{2} \times (a + l) \]
where:
- \( S_n \) is the sum of the first n terms,
- \( n \) is the number of terms,
- \( a \) is the first term,
- \( l \) is the last term.

### Step 2: Substitute the known values into the formula
We know:
- \( S_9 = 144 \)
- \( n = 9 \)
- \( l = 28 \)

Substituting these values into the formula:
\[ 144 = \frac{9}{2} \times (a + 28) \]

### Step 3: Simplify the equation
To eliminate the fraction, multiply both sides by 2:
\[ 288 = 9 \times (a + 28) \]

Now, divide both sides by 9:
\[ 32 = a + 28 \]

### Step 4: Solve for a
To find the first term \( a \), subtract 28 from both sides:
\[ a = 32 - 28 \]
\[ a = 4 \]

### Conclusion
The first term \( a \) of the A.P. is **4**.