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.

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