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 sequence, which is 2.
- To find the common difference \( D \), subtract 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 \( A_n \) of an arithmetic progression is given by:
\[ A_n = A + (n - 1) \times D \]
where:
- \( A \) is the first term,
- \( D \) is the common difference,
- \( n \) is the term number.

### Step 3: Substitute the values into the formula
We need to find the 16th term, so we set \( n = 16 \):
\[ A_{16} = A + (16 - 1) \times D \]
Substituting the known values:
\[ A_{16} = 2 + (16 - 1) \times 5 \]

### Step 4: Simplify the expression
Calculate \( 16 - 1 \):
\[ 16 - 1 = 15 \]
Now substitute this back into the equation:
\[ A_{16} = 2 + 15 \times 5 \]

### Step 5: Calculate \( 15 \times 5 \)
\[ 15 \times 5 = 75 \]

### Step 6: Add the results
Now add 2 to 75:
\[ A_{16} = 2 + 75 = 77 \]

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

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