Finding the Term of an Arithmetic Sequence
Given an arithmetic sequence with the first term and the common difference , the (or general) term is given by .
Example 1:
Find the term of the arithmetic sequence .
So,
Example 2:
Find the
term for the arithmetic sequence in which
and
.
Substitute
for
and
for
in the formula
to obtain a
system of linear equations
in terms of
and
.
Subtract the second equation from the first equation and solve for .
Then
. Solve for
.
Now use the formula to find .
.
See also: sigma notation of a series and term of a geometric sequence