The 21^st term of the A.P , whose first two terms are and is:

Here we are given the first two terms of an 𝐴. 𝑃. and we need to find its 21^st term.

In the given 𝐴. 𝑃., first term; 𝑎 =− 3 

We know that the common difference of an 𝐴𝑃 is the difference between its two consecutive terms.

⇒ Common difference; 𝑑 = 4 − (− 3)

 ⇒ 𝑑 = 7 

Using the formula 𝑇_n  = 𝑎 + (𝑛 − 1)𝑑

where 𝑎 is the first term of the 𝐴. 𝑃, 𝑑 is its common difference, and 𝑛 is the number of terms, we can find the 21^st term as follows

𝑇_n  =− 3 + (21 − 1) × 7 

𝑇_n = 137

Hence, the 21𝑠𝑡 term of the given 𝐴. 𝑃. is 137.