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Question
Write the first five terms of the following sequences whose nth terms are:
an = n2 − n + 1
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)^2 - (1) + 1`
= 1 - 1 + 1
= 1
Similarly, we find the other four terms,
Second term (n = 2)
`a_2 = (2)^2 - (2) + 1`
= 4 - 2 + 1
= 3
Third term (n = 3)
`a_3 = (3)^2 - (3) + 1`
= 9 - 3 + 1
= 7
Fourth teem (n = 4)
`a_4 = (4)^2 - (4) + 1`
= 16 - 4 + 1
= 13
Fifth term (n = 5)
`a_5 = (5)^2 - (5) + 1`
= 25 - 5 + 1
= 21
Therefore, the first five terms for the given sequence are
`a_1 = 1, a_2 = 3, a_3 = 7, a_4 = 13, a_5 = 21`
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