Question

Write a recursive rule for the sequence.
X, X, 2x, 3x, 5x, 8x, ...

Answer 1

The recursive rule for the sequence is

`a_(1)` = x

`a_(2)` = x

`a_(n)` =
`a_(n-1)` +
`a_(n-2)`

Explanation:

∵ The first term is x

∴
`a_(1)` = x

∵ The second term is x

∴
`a_(2)` = x

∵ The third term is 2x

- That means the third term is the sum of the 1st and 2nd terms

∴
`a_(3)` =
`a_(1)` +
`a_(2)`

∵ The fourth term is 3x

∴
`a_(4)` =
`a_(2)` +
`a_(3)`

∵ The fifth term is 5x

∴
`a_(5)` =
`a_(3)` +
`a_(4)`

∵ The sixth term is 8x

∴
`a_(6)` =
`a_(4)` +
`a_(5)`

From all above the sequence is Fibonacci sequence where its recursive rule is

`a_(1)` = first term

`a_(2)` = second term

`a_(n)` =
`a_(n-1)` +
`a_(n-2)`

The recursive rule for the sequence is

`a_(1)` = x

`a_(2)` = x

`a_(n)` =
`a_(n-1)` +
`a_(n-2)`