Question

1,3,9,27 what are the next 5 numbers?
and what is the nth term
please show working out

Answer 1

81, 243, 729, 2187, 6561

Explanation:

Note that the

third term 9 = 3²

fourth term 27 = 3³

Thus to obtain a particular term in the sequence we require the exponent to be one less than the terms position n in the sequence, that is

`a_(n)` =
`3^(n-1)` , thus

first term 1 →
`3^(1-1)` =
`3^(0)` = 1

The next 5 terms in the sequence are

`a_(5)` =
`3^(5-1)` =
`3^(4)` = 81

`a_(6)` =
`3^(6-1)` =
`3^(5)` = 243

`a_(7)` =
`3^(7-1)` =
`3^(6)` = 729

`a_(8)` =
`3^(8-1)` =
`3^(7)` = 2187

`a_(9)` =
`3^(9-1)` =
`3^(8)` = 6561

Answer 2

Explanation: