For some real number , the first three terms of an arithmetic sequence are
and
. What is the numerical value of the fourth term?
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The correct answer is E.
To determine the numerical value of the fourth term, first determine the value of and then apply the common difference.
Since , and
are the first three terms of an arithmetic sequence, it must be true that
, that is,
Solving
for
gives
. Substituting
for
in the expressions of the three first terms of the sequence, one sees that they are
,
, and
, respectively. The common difference between consecutive terms for this arithmetic sequence is
, and therefore, the fourth term is
.