In an A.P. 2,7, 12,……… 20th term is

Options

A. `-74`
B. `47`
C. `57`
D. `97`

Answer

To find the 20th term of the arithmetic progression (A.P.) given as 2, 7, 12, ..., we will 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 \( d \), 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:
\[ T_n = a + (n - 1) \cdot d \]
where:
- \( a \) is the first term,
- \( n \) is the term number,
- \( d \) is the common difference.

### Step 3: Substitute the values into the formula
We need to find the 20th term, so we set \( n = 20 \):
\[ T_{20} = 2 + (20 - 1) \cdot 5 \]

### Step 4: Simplify the expression
Now, calculate \( (20 - 1) \cdot 5 \):
\[ T_{20} = 2 + 19 \cdot 5 \]
\[ T_{20} = 2 + 95 \]
\[ T_{20} = 97 \]

### Final Answer
The 20th term of the A.P. is \( 97 \).

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