Question

Question 4 of 5

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used
Match each explicit formula to its corresponding recursive formula.
(8) = 5(5)(1-1)
(n) = 3 +5(n-1)
(3) = 5+3(1-1)
7(n) = 3(5)(n-1)
$(n) = 5 +5(n-1)
f(1) = 5
(*) = 3;(n - 1), for 3
(1) = 5
(n) = f(n-1) +5, for n?
f(1) = 5
f(n) = f(n-1) + 3, for n?

Answer 1

Given:

The recursive formulae.

To find:

The correct explicit formulae for the given recursive formulae.

Solution:

If the recursive formula of a GP is
`f(n)=rf(n-1), f(1)=a, n\geq 2`, then the explicit formula of that GP is:

`f(n)=ar^(n-1)`

Where, a is the first term and r is the common ratio.

The first recursive formula is:

`f(1)=5`

`f(n)=3f(n-1)` for
`n\geq 2`.

It is the recursive formula of a GP with a=5 and r=3. So, the required explicit formula is:

`f(n)=5(3)^(n-1)`

Therefore, the required explicit formula for the first recursive formula is
`f(n)=5(3)^(n-1)`.

If the recursive formula of an AP is
`f(n)=f(n-1)+d, f(1)=a, n\geq 2`, then the explicit formula of that AP is:

`f(n)=a+(n-1)d`

Where, a is the first term and d is the common difference.

The second recursive formula is:

`f(1)=5`

`f(n)=f(n-1)+5` for
`n\geq 2`.

It is the recursive formula of an AP with a=5 and d=5. So, the required explicit formula is:

`f(n)=5+(n-1)5`

`f(n)=5+5(n-1)`

Therefore, the required explicit formula for the second recursive formula is
`f(n)=5+5(n-1)`.

The third recursive formula is:

`f(1)=5`

`f(n)=f(n-1)+3` for
`n\geq 2`.

It is the recursive formula of an AP with a=5 and d=3. So, the required explicit formula is:

`f(n)=5+(n-1)3`

`f(n)=5+3(n-1)`

Therefore, the required explicit formula for the third recursive formula is
`f(n)=5+3(n-1)`.