Find the first four terms of the sequence whose nth terms are given by (ii) an = (−1)n+1 n(n + 1)

Find the first four terms of the sequence whose nth terms are given by

(ii) an = (−1)n+1 n(n + 1)

Solution :

an = (−1)n+1 n(n + 1) n = 1 =  (−1)n+1 n(n + 1) =  (−1)1+1 1(1 + 1) =  1 (2) a1  = 2	n = 2 =  (−1)n+1 n(n + 1) =  (−1)2+1 2(2 + 1) =  -1 (6) a2  = -6
n = 3 =  (−1)n+1 n(n + 1) =  (−1)3+1 3(3 + 1) =  1 (12) a3  = 12	n = 4 =  (−1)n+1 n(n + 1) =  (−1)4+1 4(4 + 1) =  -1 (20) a4  = -20

Hence the first four terms are 2, -6, 12, -20.