Answer
First Term: $a_{1}=(\frac{-1}{3})^{1}=\frac{-1}{3}$
Second Term: $a_{2}=(\frac{-1}{3})^{2}=\frac{1}{9}$
Third Term: $a_{3}=(\frac{-1}{3})^{3}=\frac{-1}{27}$
Fourth Term: $a_{4}=(\frac{-1}{3})^{4}=\frac{1}{81}$
Hundredth Term: $a_{100}=(\frac{-1}{3})^{100}$
Work Step by Step
The rule for the nth term, as previously stated, can be used to find the value of any term in the sequence that the rule is given for. This is done by entering the corresponding number of the appropriate term into the rule itself.
In exercise 8, the rule for the nth term of a specific sequence is given as: $a_{n}=(\frac{-1}{3})^{n}$
To find the first four terms, in addition to the hundredth term, simply replace "n" in the rule with the corresponding term number, and then calculate the value. The solution is as follows:
First Term: $a_{1}=(\frac{-1}{3})^{1}=\frac{-1}{3}$
Second Term: $a_{2}=(\frac{-1}{3})^{2}=\frac{1}{9}$
Third Term: $a_{3}=(\frac{-1}{3})^{3}=\frac{-1}{27}$
Fourth Term: $a_{4}=(\frac{-1}{3})^{4}=\frac{1}{81}$
Hundredth Term: $a_{100}=(\frac{-1}{3})^{100}$
