Write the first five terms of each of the following sequences whose nth terms are:
$ a_{n}=n^{2}-n+1 \quad $

Given:

\( a_{n}=n^{2}-n+1 \quad \)

To do:

We have to find the first five terms of the given sequence.

Solution:

$a_n=n^{2}-n+1$

Taking $n=1$, we get

$a_1=1^{2}-1+1=1$

Taking $n=2$, we get

$a_2=2^{2}-2+1=4-1=3$

Taking $n=3$, we get

$a_3=3^{2}-3+1=9-2=7$

Taking $n=4$, we get

$a_4=4^{2}-4+1=16-3=13$

Taking $n=5$, we get

$a_5=5^{2}-5+1=25-4=21$

Hence, the first five terms of the given sequence are $1, 3, 7, 13$ and $21$.  

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Updated on: 10-Oct-2022

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