Show that a₁ , a₂ , . . ., a_n, . . . form an AP where an is defined as below :
a_n = 3 + 4n

It is given that,

         a_n = 3 + 4n
So,    a₁ = 3 + 4(1) = 3 + 4 = 7
         a₂  = 3 + 4 (2) = 3 + 8 = 11
and    a₃ = 3 + 4(3) = 3 + 12 = 15
Now, er have following numbers :
    7, 11, 15, ...........
Since the difference between each pair of consecutive terms are constant

So, the given number forms an A. P.
Here, a = 7, d = 4,    n  = 15
We know that,