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.