Find the `15^(th)` term of the A.P with second term 11 and common difference 9.

Answer

To find the 15th term of the arithmetic progression (A.P.) with the second term as 11 and the common difference as 9, we can follow these steps:

### Step 1: Identify the given values
- Second term (A2) = 11
- Common difference (d) = 9

### Step 2: Use the formula for the nth term of an A.P.
The formula for the nth term of an A.P. is given by:
\[ A_n = A + (n - 1) \cdot d \]
where:
- \( A \) = first term
- \( n \) = term number
- \( d \) = common difference

### Step 3: Find the first term (A)
Since we know the second term (A2), we can express it using the formula:
\[ A_2 = A + (2 - 1) \cdot d \]
Substituting the known values:
\[ 11 = A + 1 \cdot 9 \]
This simplifies to:
\[ 11 = A + 9 \]

### Step 4: Solve for A
Now, we can isolate A:
\[ A = 11 - 9 \]
\[ A = 2 \]

### Step 5: Substitute A and d into the nth term formula
Now that we have the first term (A = 2), we can find the 15th term (A15):
\[ A_{15} = A + (15 - 1) \cdot d \]
Substituting the values:
\[ A_{15} = 2 + (14) \cdot 9 \]

### Step 6: Calculate A15
Now, calculate the value:
\[ A_{15} = 2 + 126 \]
\[ A_{15} = 128 \]

### Conclusion
Thus, the 15th term of the arithmetic progression is:
\[ \boxed{128} \]

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