Question

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

Answer 1

No solution is possible based on the given information.

Explanation:

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`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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].

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~