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

Answer

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

### Step 1: Identify the first term (a) and the common difference (d).
- The first term \( a = 2 \).
- The common difference \( d \) can be calculated as:
\[ d = \text{second term} - \text{first term} = 7 - 2 = 5. \]

### Step 2: Use the formula for the nth term of an AP.
The formula for the nth term of an AP is given by:
\[ a_n = a + (n - 1)d. \]
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.
We need to find the 16th term (\( n = 16 \)):
\[ a_{16} = a + (16 - 1)d. \]
Substituting the known values:
\[ a_{16} = 2 + (15)(5). \]

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

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

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