a) Sequence: 11, 16, 21, ...
In this case, the sequence is arithmetic, because it has a defined pattern as a common difference, in specific we have each number separated by +5.
To obtain the formula of an arithmetic sequence we have the equation:
[tex]a_n=a_1+(n-1)d[/tex]
Where d is a common difference.
So if we reply with the numbers we have:
[tex]a_n=11+(n-1)5=5n+6[/tex]
Then the correct answer is:
Arithmetic sequence with the formula:
[tex]a_n=5n+6[/tex]
b) sequence: 20, 40, 100, ...
In this case, the sequence is geometric because we have a common factor that determines the sequence, in specific this common factor is x5.
To obtain the formula of an arithmetic sequence we have the equation:
[tex]a_n=a_1(r^{n-1})[/tex]
Where r represents the common factor of the sequence.
Then we reply:
[tex]a_n=4(5^{n-1})[/tex]
Then the correct answer is:
Geometric sequence with the formula:
[tex]a_n=4(5^{n-1})[/tex]
