The rule for the nth terms is: a_n=13n-5
Further explanation:
First of all we have to decide whether it is an arithmetic sequence or geometric sequence. It is decided based upon common difference or common ratio.
common difference is the difference between two consecutive terms of an arithmetic sequence while common ratio is the ratio between consecutive terms of a geometric sequence.
Here
[tex]a_1=8\\a_2=21\\a_3=34\\a_4=47\\a_5=60.....[/tex]
Common difference:
[tex]d=a_2-a_1=21-8=13\\a_3-a_2=34-21=13[/tex]
As the common difference is same, the given sequence is an arithmetic sequence
The general formula for arithmetic sequence is:
[tex]a_n=a_1+(n-1)d[/tex]
Here
a1=8
d=13
[tex]a_n=8+(n-1)13\\=8+13n-13\\=13n-5[/tex]
The rule for the nth terms is: a_n=13n-5
Keywords: Arithmetic sequence, Common difference
Learn more about arithmetic sequence:
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