Question

In a sequence, the nth term is a, = n²-1, n ∈ N. Show that it is not an A.P.

Answer 1

Answer:

Sn = 3 n² + 4 n

Tn = Sn - S_n-1 

     = 3 n² + 4 n - 3 (n-1)² - 4 (n-1)

     =  6 n + 1 

d = Tn - T_n-1 =  6 n + 1 - 6(n-1) - 1 = 6

Since  d = 6 = constant, The sequence is an AP.

Answer 2

Answer:

The formula of the last term of AP = S= n\2 (a+l)