Question

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

a_n = 3ⁿ

Answer 1

`a_n = 3^n`

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 = 3^(1)`

= 3

Similarly, we find the other four terms,

Second term (n = 2)

`a_2 = 3^(2)`

= (3)(3)

= 9

Third term (n = 3)

`a_3 = 3^(3)`

= (3)(3)(3)

= 27

Fourth term (n = 4)

`a_4 = 3^(4)`

= (3)(3)(3)(3)

= 81

Fifth term (n = 5)

`a_5 = 3^(5)`

= (3)(3)(3)(3)(3)

= 243

Therefore, the first five terms for the given sequence are

`a_1 = 3, a_2 = 9, a_3 = 27, a_4 = 81, a_5 = 243`