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Question
Write the first five terms of the following sequences whose nth terms are:
`a_n = (2n - 3)/6`
Solution
`a_n = (2n - 3)/6`
Here, the nth term is given by the above expression. So, to find the first term we use n = 1 we get
`a_1 = (2(1) - 1)/6`
`= (2 -3)/6`
`= (-1)/6`
Similarly, we find the other four terms,
Second term (n = 2)
`a_2 = (2(2) - 3)/6`
`= (4 - 3)/6`
`= 1/6`
Third term (n = 3)
`a_3 = (2(3) - 3)/6`
`= (6 - 3)/6`
= 3/6
=1/2
Fourth term (n = 4)
`a_4 = (2(4) -3)/6`
`= (8 -3)/6`
`=5/6`
Fifth term (n = 5)
`a_5 = (2(5) -3)/6`
= (10 - 3)/6
= 7/6
Therefore, the first five terms of the given A.P are
`a_1 = (-1)/6, a_2 = 1/6 , a_3 = 1/2, a_4 = 5/6, a_5 = 7/6`
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