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Question
Write the first five terms of the following sequences whose nth terms are:
`a_n = (n(n - 2))/2`
Solution
Here, the nth term is given by the above expression. So, to find the first term we use n = 1, we get
`a_1 = (1(1 - 2))/2`
`= (-1)/2`
Similarly, we find the other four terms,
Second term (n = 2)
`a_2 = (2(2 - 2))/2`
`= (2(0))/2`
= 0
Third term (n = 3)
`a_3 = (3(3 - 2))/2`
`= (3(1))/2`
`= 3/2`
Fourth term (n = 4)
`a_4 = (4(4 - 2))/2`
`= (4(2))/2`
`= 8/2`
= 4
Fifth term (n = 5)
`a_5 = (5(5 -2))/2`
`= (5(3))/2`
= 15/2
Therefore, the first five terms for the given sequence are
`a_1 = (-1)/2 , a_2 =0, a_3 = 3/2, a_4= 4, a_5 = 15/2`
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