In the sequence 3, 18, 13, 18, what term of the series is the number 2218?

Obviously the given sequence is not an arithmetic sequence
since there is no constant term #k# such that
#color(white)("XXX")3+k=18#
and
#color(white)("XXX")18+k=13#

Similarly the given sequence is not a geometric sequence
since there is no constant term #m# such that
#color(white)("XXX")3xxm=18#
and
#color(white)("XXX")18xxm=13#

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Other possibilities that might be considered

If the sequence is defined as:
#a_n={(3+((n-1)/2xx10),color(white)("xx"),"for " n" odd"), (18,,"for " n" even"):}#
then
#color(white)("XXX")# no term ends in the digit #8# so no term could be #2218#

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If the sequence were defined by the cubic equation:
#a_n= 5n^3-25n^2+35n+3color(white)("xxxx")n in [0,+oo)#
then generation of the given terms would be possible
but evaluations of this equation has no solution with #a_n=2218#
[I have omitted derivation and evaluation of this cubic as beyond the scope of this question... ask if required].

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