Question

Write the first five terms of the following sequences whose nth terms are:

`a_n = (2n - 3)/6`

Answer 1

`a_n = (2n - 3)/6`

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 = (2(1) - 1)/6`

`= (2 -3)/6`

`= (-1)/6`

Similarly, we find the other four terms,

Second term (n = 2)

`a_2 = (2(2) - 3)/6`

`= (4 - 3)/6`

`= 1/6`

Third term (n = 3)

`a_3 = (2(3) - 3)/6`

`= (6 - 3)/6`

= 3/6

=1/2

Fourth term (n = 4)

`a_4 = (2(4) -3)/6`

`= (8 -3)/6`

`=5/6`

Fifth term (n = 5)

`a_5 = (2(5) -3)/6`

= (10 - 3)/6

= 7/6

Therefore, the first five terms of the given A.P are

`a_1 = (-1)/6, a_2 = 1/6 , a_3 = 1/2, a_4 = 5/6, a_5 = 7/6`