The 21st term of the AP whose first two terms are –3 and 4 is

To find the 21st term of the arithmetic progression (AP) whose first two terms are –3 and 4, follow these steps:

1. Identify the first term (a) and the common difference (d) of the AP.

   • The first term (a) is –3.
   • The second term is 4.

2. Calculate the common difference (d) using the first two terms.

   • d = second term - first term
   • d = 4 - (–3)
   • d = 4 + 3
   • d = 7

3. Use the formula for the nth term of an AP, which is given by:

   • $a_n = a + (n - 1) \cdot d$

4. Substitute the values of a, d, and n into the formula to find the 21st term (a_21).

   • $a_{21} = a + (21 - 1) \cdot d$
   • $a_{21} = -3 + 20 \cdot 7$
   • $a_{21} = -3 + 140$
   • $a_{21} = 137$

Therefore, the 21st term of the AP is 137.