Question

Complete the pattern 1/27, 1/9, 1/3, 1

Answer 1

1. Let the
`n^(th)` term of the sequence be
`u_(n)`

2. The first term
`u_(1)`=1/27, second term
`u_(2)`=1/9 and so on

3. so


`u_(1)= (1)/(27)= (1)/( 3^(3) )= 3^(-3)`


`u_(2)= (1)/(9)= (1)/( 3^(2) )= 3^(-2)`


`u_(3)= (1)/(3)= (1)/( 3^(1) )= 3^(-1)`


`u_(4)= 3^(0)`

so by now it is clear that the general rule is
`u_(n)= 3^(n-4)`

so the next term,
`u_(4)` is
`u_(5)= 3^(5-4)=3^(1)=3`