Question

Write the rule for the nth term of each sequence.

Answer 1

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,

$a_1 = 7\\a_2 = 4\\a_3 = 1\\d = a_2 - a_1 = 4-7 = -3\\d = a_3 - a_2 = 1-4 = -3$

The explicit rule for an arithmetic sequence is:

$a_n = a_1 + (n-1)d$

Putting the value of a1 and d

$a_n = 7 + (n-1)(-3)\\a_n = 7 -3n+3\\a_n = 10-3n$

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,

$a_1 = -11\\a_2 = -3\\a_3 = 5\\d = a_2 - a_1 = -3+11 = 8\\d = a_3 - a_2 = 5+3 = 8$

The explicit rule for an arithmetic sequence is:

$a_n = a_1 + (n-1)d$

Putting the value of a1 and d

$a_n =-11 + (n-1)(8)\\a_n = -11 +8n-8\\a_n = -19+8n$

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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