Answer:
-22, -28
[tex]\displaystyle \large{a_n=-6n+2}[/tex]
Step-by-step explanation:
Given:
- Sequence -4, -10, -16, __, __
Since the sequence doesn’t have common ratio, find common difference by subtracting the next term with previous term:
-10-(-4) = -10+4 = -6
-16-(-10):= -16+10 = -6
Therefore, there is a common difference which is -6. Hence, this sequence is arithmetic sequence.
To find next term, add the term with common difference:
-16-6 = -22
-22-6 = -28
Therefore, the finished sequence is -4, -10, -16, -22, -28
Next, find the rule which is the general term (nth term) for this sequence. The formula/rule is:
[tex]\displaystyle \large{a_n=a_1+(n-1)d}[/tex]
Where [tex]\displaystyle \large{a_n}[/tex] is nth term, [tex]\displaystyle \large{a_1}[/tex] is first term and [tex]\displaystyle \large{d}[/tex] is common difference. We know that first term is -4 and common difference is -6. Hence:
[tex]\displaystyle \large{a_n=-4+(n-1)(-6)}\\\\\displaystyle \large{a_n=-4-6n+6}\\\\\displaystyle \large{a_n=-6n+2}[/tex]
Thus, the rule is [tex]\displaystyle \large{a_n=-6n+2}[/tex]
