Question

Write the first five terms of each of the following sequences whose $n$th terms are: $a_n=\frac{n(n-2)}{2}$

Answer 1

$a_n=\frac{n(n-2)}{2}...................eq\left(1\right)$

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

$⟹a_1=\frac{1(1-2)}{2}$

$⟹a_1=\frac{1(-1)}{2}$

$⟹a_1=-\frac{1}{2}$

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

$⟹a_2=\frac{2(2-2)}{2}$

$⟹a_2=\frac{2\left(0\right)}{2}$

$⟹a_2=\frac{0}{2}$

$⟹a_2=0$

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

$⟹a_3=\frac{3(3-2)}{2}$

$⟹a_3=\frac{3\left(1\right)}{2}$

$⟹a_3=\frac{3}{2}$

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

$⟹a_4=\frac{4(4-2)}{2}$

$⟹a_4=\frac{4\left(2\right)}{2}$

$⟹a_4=\frac{8}{2}$

$⟹a_4=4$

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

$⟹a_5=\frac{5(5-2)}{2}$

$⟹a_5=\frac{5\left(3\right)}{2}$

$⟹a_5=\frac{15}{2}$