Question

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

a_n = n² − n + 1

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)^2 - (1) + 1`

= 1 - 1 + 1

= 1

Similarly, we find the other four terms,

Second term (n = 2)

`a_2 = (2)^2 - (2) + 1`

= 4 - 2 + 1

= 3

Third term (n = 3)

`a_3 = (3)^2 - (3) + 1`

= 9 - 3 + 1

= 7

Fourth teem  (n = 4)

`a_4 = (4)^2 - (4) + 1`

= 16 - 4 + 1

= 13

Fifth term (n = 5)

`a_5 = (5)^2 - (5) + 1`

= 25 - 5 + 1

= 21

Therefore, the first five terms for the given sequence are

`a_1 = 1, a_2 = 3, a_3 = 7, a_4 = 13, a_5 = 21`