We can generatethe termsfor this rule as follows:
n 1 2 3 4 ...
...Example 2
Considerthe sequencerule.
The termsof the sequenceare:
...
...You can also find rule for a sequence.
Example 3
Find the rule for the sequencebelow.
n 1 2 3 4 ...
...Lookat eachterm in termsof its index.The numeratorof eachterm matchesthe index.The denominator
is one morethan the index.So far, we can writethe formulaanas. However, we are not done.
Noticethat eacheven-indexedterm has a negativesign.This meansthat all of termsof the sequencehave
a powerof –1. The powersof –1 alternatebetweenodd and even.Usually, alternatingpowersof –1 can be
denoteby (-1)nor (-1)n + 1. Sincethe termsare negativefor evenindices,we use (-1)n + 1. Thus,the
rule for the sequenceis. You can checkthe rule by findingthe first few termsof the sequence
.Limitof a Sequence
We are interestedin the behaviorof the sequenceas the valueofngets very large.Manytimesa sequence
will get closerto a certainnumber, orlimit,asngets large.Findingthe limit of a sequenceis very similar
to findingthe limit of a function.Let’s look at somegraphsof sequences.
Example 4
Find the limit of the sequence asngoesto infinity.