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Question
Find the first four terms of the sequence whose nth terms are given by an = (–1)n+1 n(n + 1)
Solution
an = (–1)n+1 n(n + 1)
a1 = (–1)1+1 (1) (1 + 1)
= (–1)2 (1) (2) = 2
a2 = (–1)2+1 (2) (2 + 1)
= (–1)3 (2) (3)= – 6
a3 = (–1)3+1 (3) (3 + 1)
= (–1)4 (3) (4) = 12
a4 = (–1)4+1 (4) (4 + 1)
= (–1)5 (4) (5) = – 20
∴ The first four terms are 2, – 6, 12, – 20, …
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