Question

Classify the sequences as arithmetic geometric, Fibonacci -5,0,10,15,25

Answer 1

`\text{If a, b, c are an arithmetic sequence then}\ a+c=2b.\\\\\text{If a, b, c are a geometric sequence, then}\ ac=b^2\\\\\text{We have -5, 0, 10, 15, 25}\\\\a=-5,\ b=0,\ c=10\\\\a+c=-5+10=5\\2b=2(0)=0\\\text{It's not an arithmetic sequence}\\\\ac=(-5)(10)=-50\\b^2=0^2=0\\\text{It's not a geometric sequence}\\\\\text{Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21, ...}\\\\Answer:\ -5,\ 0,\ 10,\ 15,\ 25\ \text{is different sequence}.`

Answer 2

It is arithmetic.

It starts at - 5,

the next item is 0 then 5 and next is 15 ...

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It isn't geometric. You are not multiplying by 5

The second term must be and not- 5 * 5 = - 25

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A Fibonacci series adds the previous two terms together to get the next term

Usually it starts at 0, but it doesn't need to.

0,1,1,2,3,5,8,13,21,34 ....