In the arithmetic sequence , determine the tenth term from the end.
To find the tenth term from the end, we first need to find the formula for the term. Remember the formula for the term of an arithmetic sequence is
where is the first term and is the common difference. In the series we have,
and . Therefore,
Now we need to know how many terms there are in the series. We know that for the last term, . Therefore, using the formula for the term, we can find as follows:
Therefore, the tenth term from the end will be term number 27.
Remember that the second term from the end is term (i.e., the tenth term from the end will be ).
Using the formula, we can find this term.