Find the `16^(th)` term of the AP: 2, 7, 12, 17….. .

Answer

To find the 16th term of the arithmetic progression (AP) given as 2, 7, 12, 17, we can follow these steps:

### Step 1: Identify the first term (A) and the common difference (d)
- The first term \( A \) is the first number in the AP, which is \( 2 \).
- The common difference \( d \) is found by subtracting the first term from the second term:
\[ d = 7 - 2 = 5 \]

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

### Step 3: Substitute the values into the formula
To find the 16th term (\( A_{16} \)):
\[ A_{16} = A + (16 - 1) \cdot d \]
Substituting the values of \( A \) and \( d \):
\[ A_{16} = 2 + (15) \cdot 5 \]

### Step 4: Calculate the expression
Now, calculate \( 15 \cdot 5 \):
\[ 15 \cdot 5 = 75 \]
Now substitute back into the equation:
\[ A_{16} = 2 + 75 = 77 \]

### Final Answer
Thus, the 16th term of the AP is \( 77 \).

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