Determine the ` 12^(th)` term of the AP, 5, 8, 11, 14, . . . . . .

Answer

To determine the 12th term of the arithmetic progression (AP) given as 5, 8, 11, 14, ..., we can follow these steps:

### Step 1: Identify the first term (A) and the common difference (d)
The first term \( A \) of the AP is the first number in the sequence, which is:
\[ A = 5 \]

To find the common difference \( d \), we subtract the first term from the second term:
\[ d = A_2 - A_1 = 8 - 5 = 3 \]

### Step 2: Use the formula for the nth term of an AP
The formula for the nth term \( A_n \) of an arithmetic progression is given by:
\[ A_n = A + (n - 1) \cdot d \]

### Step 3: Substitute \( n = 12 \) into the formula
We need to find the 12th term, so we substitute \( n = 12 \) into the formula:
\[ A_{12} = A + (12 - 1) \cdot d \]
\[ A_{12} = 5 + (11) \cdot 3 \]

### Step 4: Calculate the value
Now, we will calculate the value:
\[ A_{12} = 5 + 33 \]
\[ A_{12} = 38 \]

### Conclusion
Thus, the 12th term of the AP is:
\[ A_{12} = 38 \]

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