Rule for sequence a is: a_n = 10-3n
Rule for sequence b is: a_n = -19+8n
Step-by-step explanation:
a.)7, 4, 1, -2, ...
First of all we have to find the common difference. Common difference is the difference between consecutive terms of an arithmetic sequence
Here,
[tex]a_1 = 7\\a_2 = 4\\a_3 = 1\\d = a_2 - a_1 = 4-7 = -3\\d = a_3 - a_2 = 1-4 = -3[/tex]
The explicit rule for an arithmetic sequence is:
[tex]a_n = a_1 + (n-1)d[/tex]
Putting the value of a1 and d
[tex]a_n = 7 + (n-1)(-3)\\a_n = 7 -3n+3\\a_n = 10-3n[/tex]
b.)-11, -3, 5, 13, ...
First of all we have to find the common difference. Common difference is the difference between consecutive terms of an arithmetic sequence
Here,
[tex]a_1 = -11\\a_2 = -3\\a_3 = 5\\d = a_2 - a_1 = -3+11 = 8\\d = a_3 - a_2 = 5+3 = 8[/tex]
The explicit rule for an arithmetic sequence is:
[tex]a_n = a_1 + (n-1)d[/tex]
Putting the value of a1 and d
[tex]a_n =-11 + (n-1)(8)\\a_n = -11 +8n-8\\a_n = -19+8n[/tex]
Hence,
Rule for sequence a is: a_n = 10-3n
Rule for sequence b is: a_n = -19+8n
Keywords: Arithmetic sequence, common difference
Learn more about arithmetic sequence at:
- brainly.com/question/2048256
- brainly.com/question/2115122
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