The explicit rule for given sequence is:
[tex]a_n=2+10n[/tex]
Further explanation:
We have to determine first of all if the sequence is arithmetic or geometric.
Given sequence is:
12,22,32,42
[tex]a_1=12\\a_2=22\\a_3=32\\.......\\Let\\d=Common\ difference\\d=a_2-a_1=22-12=10\\d=a_3-a_2=32-22=10[/tex]
The common difference is 10 which is same for all consecutive terms. So the sequence is an arithmetic sequence.
The general formula for arithmetic sequence is:
[tex]a_n=a_1+(n-1)d\\Here,\\a_n\ is\ the\ nth\ term\\a_1\ is\ the\ first\ term\\d\ is\ the\ common\ difference[/tex]
Putting the values of a1 and d
[tex]a_n= 12+(n-1)(10)\\a_n=12+10n-10\\a_n=2+10n[/tex]
The explicit rule for given sequence is:
[tex]a_n=2+10n[/tex]
Keywords: Arithmetic sequence, Common Difference
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