Question

Question 2 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,

Answer 1

From Edmentum :)

Answer 2

Given:

The different recursive formulae.

To find:

The explicit formulae for the given recursive formulae.

Solution:

The recursive formula of an arithmetic sequence is
`f(n)=f(n-1)+d, f(1)=a,n\geq 2` and the explicit formula is
`f(n)=a+(n-1)d`, where a is the first term and d is the common difference.

The recursive formula of a geometric sequence is
`f(n)=rf(n-1), f(1)=a,n\geq 2` and the explicit formula 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)=f(n-1)+5` for
`n\geq 2`.

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:

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

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

Therefore, the correct option is A, i.e.,
`f(n)=5+5(n-1)`.

The second recursive formula is:

`f(1)=5`

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

It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:

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

Therefore, the correct option is F, i.e.,
`f(n)=5(3)^(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 arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:

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

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

Therefore, the correct option is D, i.e.,
`f(n)=5+3(n-1)`.