Question

What are the explicit and recursive formulas for the sequence 10,15,22.5,33.75,..?

if you can please help with both 14 and 15 thank you ​

Answer 1

14- The given sequence has common ratio =
`(1)/(2)`, so it is a geometric sequence.

15- explicit :
`a_(n)=10(1.5)^(n-1)`, recursive :
`a_(n)=1.5* a_(n-1)`

Explanation:

Ques 14: We have the sequence,
`18,9,(9)/(2),(9)/(4),(9)/(8),...`.

So, we will find the common ratio of the given sequence,

i.e. Common ratio =
`(9)/(18)=((9)/(2))/(9)=..=(1)/(2)`

Thus, we have,

The given sequence has common ratio =
`(1)/(2)`, so it is a geometric sequence.

Ques 15: We have the sequence,
`10,15,22.5,33.75,...`

As, the common ratio of the given sequence =
`(15)/(10)=(22.5)/(15)=...=1.5`

Thus, the explicit form is given by,
`a_(n)=a_(1)(r)^(n-1)` i.e.
`a_(n)=10(1.5)^(n-1)`.

Also, the recursive form is given by,
`a_(n)=r* a_(n-1)` i.e.
`a_(n)=1.5* a_(n-1)`.