Question
Write the first five terms of the following sequences whose $n^{th}$ terms are:
$a_n = n^2 - n + 1.$
$a_n = n^2 - n + 1.$
✓
Answer
$a_n = n^2 - n + 1$.Here, the $n^{th}$ term is givne by the above expression. So, to find the first term we use $n = 1$, we get,
$a_1 = (1)^2 - (1) + 1$
$= 1 - 1 + 1$
$a_2 = (2)^3 - (2) + 1$
$= 4 - 2 + 1$
$= 3$
Third term $(n = 3),$
$a_4 = (4)^2 - (4) + 1$
$= 16 - 4 + 1$
$= 13$
Fifth term $(n = 5),$
$a_5 = (5)^2 - (5) + 1$
$= 25 - 5 + 1$
$= 21$
Therefore, the first terms for the given sequence are $a_1 = 1, a_2 = 3, a_3 = 7, a_4 = 13, a_5 = 21$.
$a_1 = (1)^2 - (1) + 1$
$= 1 - 1 + 1$
$= 1$
Similarly, we find the other four terms,
Second term $(n = 2),$Similarly, we find the other four terms,
$a_2 = (2)^3 - (2) + 1$
$= 4 - 2 + 1$
$= 3$
Third term $(n = 3),$
$a_3 = (3)^2 - (3) + 1$
$= 9 - 3 + 1$
$= 7$
Fourth term $(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 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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