The sequence is an illustration of an arithmetic sequence.
The nth rule is: (d) [tex]a_n = 3n -8[/tex]
We have:
[tex]a_1 = -5[/tex] -- the first term
Next, we calculate the common difference (d)
[tex]d = a_2 - a_1[/tex]
So, we have:
[tex]d = -2 -(-5)[/tex]
[tex]d = -2 +5[/tex]
[tex]d = 3[/tex]
The nth rule is calculated using:
[tex]a_n = a_1 + (n - 1)d[/tex]
So, we have:
[tex]a_n =-5 + (n - 1) \times 3[/tex]
Open bracket
[tex]a_n =-5 + 3n - 3[/tex]
Collect like terms
[tex]a_n = 3n -5- 3[/tex]
[tex]a_n = 3n -8[/tex]
Hence, the nth rule is: [tex]a_n = 3n -8[/tex]
Read more about arithmetic sequence at:
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