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AveGali [126]
3 years ago
11

Sarah is collecting recyclables for a science project. on the first day she collects 35 recyclable objects. on the second day sh

e 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.
Mathematics
2 answers:
valkas [14]3 years ago
8 0

Answer:

1). Arithmetic mean

2). Recursive formula: a_{n}=a_{n-1}+17

Step-by-step 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

Svet_ta [14]3 years ago
4 0
The scneario here expressed is an aritmetic sequence because it can be explained like this: 

<span><span><span>a1</span>=35
</span><span><span>an</span>=<span>a<span>n−1</span></span>+<span>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</span></span></span>
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