Option (A) the first sequence is geometric because there is a common ratio of 2 and the second sequence is arithmetic because there is a common difference of 7 is the correct answer.
What is a number pattern?
Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. A recursive pattern rule is a pattern rule that tells you the start number of a pattern and how the pattern continues.
For the given situation,
First sequence: 5, 10, 20, 40..
Second sequence: 8, 15, 22, 29, ...
Now consider the first sequence: 5, 10, 20, 40..
Here, when we divide the second number by first number, we get the common ratio as 2.
⇒ [tex]\frac{10}{5}=2[/tex]
⇒ [tex]\frac{20}{10}=2[/tex]
⇒ [tex]\frac{40}{20}=2[/tex]
Thus the first sequence follows a geometric progression with common ratio 2.
Now consider the second sequence: 8, 15, 22, 29, ...
Here, when we subtract the first term is subtracted from the second term, the common difference is 7.
⇒ [tex]15-8=7[/tex]
⇒ [tex]22-18=7[/tex]
⇒ [tex]29-22=7[/tex]
Hence we can conclude that option (A) the first sequence is geometric because there is a common ratio of 2 and the second sequence is arithmetic because there is a common difference of 7 is the correct answer.
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