The explicit rule for the arithmetic sequence on which the series is based is an = 12 + (n - 1) * 6
How to determine the explicit rule of a sequence?
Series are sum of sequences. The nth term of an arithmetic series is expressed as:
an = a + (n - 1)d
where
a is the first term = 12
n is the number of terms
d is the common difference = 18 - 12 = 24 - 18 = 6
Substitute
an = 12 + (n - 1) * 6
Hence the explicit rule for the arithmetic sequence on which the series is based is an = 12 + (n - 1) * 6
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