Question

Sarah is collecting recyclables for a science project. on the first day she collects 35 recyclable objects. on the second day she has a total of 52 recyclables. on the third day she has a total of 69 recyclables. determine if the scenario describes an arithmetic or a geometric sequence. then, write the recursive formula for the sequence described.

Answer 1

1). Arithmetic mean

2). Recursive formula:
`a_(n)=a_(n-1)+17`

Explanation:

Sarah is collecting recyclables for a science project. On day 1 she collects 35 recyclable objects, on day 2 she collected 52 and on day 3 she collected 69 recyclables.

So, sequence of recyclable objects formed was 35, 52, 69 .........

If this sequence is an arithmetic sequence then each successive term will have a common difference and if it's a geometric sequence then there will be a common ratio in each successive term.

Now common difference =
`d=T_(2)-T_(1)=T_(3)-T_(2)`

52 - 35 = 17

69 - 52 = 17

Therefore, it's an arithmetic sequence.

Now we know the recursive formula of an arithmetic sequence is

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

Here d = 17

So, recursive formula will be
`a_(n)=a_(n-1)+17`

Answer 2

The scneario here expressed is an aritmetic sequence because it can be explained like this:

a1=35
an=an−1+17

So all the variables can fit in and will be better explained than a geometric sequence in which you need a common ratio and that is not needed in this case