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Need help please i need to be able to solve this

Need help please i need to be able to solve this-example-1
User Aleph
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Answer: E

Given the sequence:

1, 6, 7, 13, ...

Let us check whether it is Arithmetic, Geometric, or Fibonacci.

Arithmetic Sequence has a common difference. To check whether the sequence is the arithmetic sequence or not, let us try to get its common difference.

We will do this by subtracting a term from the previous term.

6 - 1 = 5

7 - 6 = 1

13 - 7 = 6

As we can see, their differences are not common, therefore, it is not an example of an arithmetic sequence.

Next, let's check if it is an example of a Geometric Sequence. Geometric sequences have a common ratio.

To do this, we will divide a term by the previous term.

6/1 = 6

7/6 = 1 1/6

13 / 7 = 1 6/7

As we can see, they do not have a common ratio, therefore, it is not an example of a Geometric Sequence.

A Fibonacci sequence works by having the next number in the sequence by adding up the two numbers before it.

1 + 6 = 7

7 + 6 = 13

As we can see, it lines up with the sequence, therefore, the given sequence is an example of a Fibonacci Sequence.

To find the next term, we will just add 7 and 13, and that will give us:

7 + 13 = 20

Therefore, the answer is E.

User Fatih Acet
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