For an A.P. 2, 7, 12, ……… `12th` term will be :

Options

A. 55
B. 57
C. 59
D. `53`

Answer

To find the 12th term of the arithmetic progression (A.P.) given by 2, 7, 12, ..., 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:
\[ a = 2 \]

To find the common difference \( d \), we subtract the first term from the second term:
\[ d = 7 - 2 = 5 \]

### Step 2: Use the formula for the nth term of an A.P.
The formula for the nth term \( T_n \) of an A.P. is given by:
\[ T_n = a + (n - 1) \cdot d \]

### Step 3: Substitute the values into the formula
We need to find the 12th term, so we set \( n = 12 \):
\[ T_{12} = a + (12 - 1) \cdot d \]
\[ T_{12} = 2 + (11) \cdot 5 \]

### Step 4: Calculate the value
Now, we calculate:
\[ T_{12} = 2 + 55 \]
\[ T_{12} = 57 \]

### Conclusion
The 12th term of the A.P. is:
\[ \boxed{57} \]

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