Question

Write the first five terms of the following sequences whose nth term is:

`a_n = (n(n - 2))/2`

Answer 1

Here, the n^th term is given by the above expression. So, to find the first term we use  n = 1, we get

`a_1 = (1(1 - 2))/2`

`= (-1)/2`

Similarly, we find the other four terms,

Second term (n = 2)

`a_2 = (2(2 - 2))/2`

`= (2(0))/2`

= 0

Third term (n = 3)

`a_3 = (3(3 - 2))/2`

`= (3(1))/2`

`= 3/2`

Fourth term (n = 4)

`a_4 = (4(4 - 2))/2`

`= (4(2))/2`

`= 8/2`

= 4

Fifth term (n = 5)

`a_5 = (5(5 -2))/2`

`= (5(3))/2`

`= 15/2`

Therefore, the first five terms for the given sequence are

`a_1 = (-1)/2, a_2 =0, a_3 = 3/2, a_4= 4, a_5 = 15/2`