Question

the sum of n terms of a sequence is 3n square plus 4n.find the nth term and show that the sequence is an ap

Answer 1

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.