Question

Write the first five terms of each of the following sequences whose $n$th terms are:$a_n=n^2-n+1$

Answer 1

$a_n=n^2-n+1...................eq\left(1\right)$

1) To find the first term of sequence $\left(a_1\right)$ put n=1 in eq(1)

$⟹a_1=1^2-1+1$

$⟹a_1=1-1+1$

$⟹a_1=1$

2) To find the second term of sequence $\left(a_2\right)$ put n=2 in eq(1)

$⟹a_2=2^2-2+1$

$⟹a_2=4-2+1$

$⟹a_2=3$

3) To find the third term of sequence $\left(a_3\right)$ put n=3 in eq(1)

$⟹a_3=3^2-3+1$

$⟹a_3=9-3+1$

$⟹a_3=7$

4) To find the fourth term of sequence $\left(a_4\right)$ put n=4 in eq(1)

$⟹a_4=4^2-4+1$

$⟹a_4=16-4+1$

$⟹a_4=13$

5) To find the fifth term of sequence $\left(a_5\right)$ put n=5 in eq(1)

$⟹a_5=5^2-5+1$

$⟹a_5=25-5+1$

$⟹a_5=21$