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Question
If the nth term an of a sequence is given by an = n2 − n + 1, write down its first five terms.
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Solution
\[\text { Given } : a_n = n^2 - n + 1\]
\[\text { For } n = 1, a_1 = 1^2 - 1 + 1 \]
\[ = 1\]
\[\text { For } n = 2, a_2 = 2^2 - 2 + 1 \]
\[ = 3\]
\[\text { For n = 3, a_3 = 3^2 - 3 + 1 \]
\[ = 7\]
\[\text { For } n = 4, a_4 = 4^2 - 4 + 1 \]
\[ = 13\]
\[\text { For }n = 5, a_5 = 5^2 - 5 + 1 \]
\[ = 21\]
Thus, the first five terms of the sequence are 1, 3, 7, 13, 21.
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