20th term of the A.P. 2 , 7, 12,………. is :

Options

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

Answer

To find the 20th term of the arithmetic progression (A.P.) given as 2, 7, 12, ..., we can use the formula for the nth term of an A.P.:

**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 A.P.**
- The formula for the nth term \( T_n \) of an A.P. is given by:
\[ T_n = a + (n - 1) \cdot d. \]
- Here, we need to find the 20th term, so \( n = 20 \).

**Step 3: Substitute the values into the formula.**
- Plugging in the values we have:
\[ T_{20} = 2 + (20 - 1) \cdot 5. \]

**Step 4: Simplify the expression.**
- Calculate \( (20 - 1) \):
\[ 20 - 1 = 19. \]
- Now substitute this back into the equation:
\[ T_{20} = 2 + 19 \cdot 5. \]

**Step 5: Calculate \( 19 \cdot 5 \).**
- This gives:
\[ 19 \cdot 5 = 95. \]

**Step 6: Add the first term to the product.**
- Finally, calculate:
\[ T_{20} = 2 + 95 = 97. \]

Thus, the 20th term of the A.P. is **97**.