Answer:
Arithmetic sequence states that it is a sequence of numbers such that the difference of any two successive members of the sequence is a constant(d)
The rule for the sequence is:
[tex]a_n = a+(n-1)d[/tex]
where a is the first term , d is the common difference and n is the number of terms.
Given the pattern: 101, 94, 87, 80.
First term (a) = 101
This pattern is an arithmetic sequence with common difference(d) = -7
Since,
94 -101 = -7
87 -94 = -7
80- 87 = -7
The rule for this pattern is;
[tex]a_n = 101+(n-1)(-7)= 101 -7n + 7[/tex]
or
[tex]a_n = 108 -7n[/tex]
Therefore, the rule for this pattern is, [tex]a_n = 108 -7n[/tex] where n is the number of term.
