4.18.7 Practice

Complete the following questions to practice the skills you have learned in this lesson.

1. Find the value of each specified term of the arithmetic sequences below. Hint: Enter your answers as an integer only. Do not include commas or periods.


1. Find the ${21}^{st}$ term of a sequence where the first term is $3$ and the common difference is $8$.
   

2. Find the ${30}^{th}$ term of a sequence where the first term is $–14$ and the common difference is $5$.

3. Find the ${16}^{th}$ term of a sequence where the first term is $11$ and the common difference is $–6$.

2. Find the value of each specified term of the geometric sequences below. Hint: Enter your answers as integers only. Do not include commas or periods.


1. Find the ${11}^{th}$ term given the first term is $8$ and the common ratio is $3$.
   

2. Find the ${10}^{th}$ term given the first term is $–6$ and the common ratio is $–2$.

3. A sequence is defined recursively by $f_1=-<!--\; -\; -->6,f_n=f_{n-<!--\; -\; -->1}-<!--\; -\; -->2$, for $n\ge 2$. Which of the following gives the $n^{th}$ term for $n\ge 0$?

1. $a_n=-<!--\; -\; -->6+(n)(-<!--\; -\; -->2)$
2. $a_n=-<!--\; -\; -->6+(n-<!--\; -\; -->1)+(-<!--\; -\; -->2)$
3. $a_n=-<!--\; -\; -->6+(n-<!--\; -\; -->1)(-<!--\; -\; -->2)$
4. $a_n=-<!--\; -\; -->2+(n-<!--\; -\; -->1)(-<!--\; -\; -->6)$

4. A sequence is defined recursively by $f_1=-<!--\; -\; -->20,f_n=f_{(n-<!--\; -\; -->1)}+5$ for $n\ge 2$. Which of the following is the $n^{th}$ term?

1. $a_n=5+(n-<!--\; -\; -->1)(-<!--\; -\; -->20)$
2. $a_n=-<!--\; -\; -->20+(n-<!--\; -\; -->1)(5)$
3. $a_n=-<!--\; -\; -->20+(n-<!--\; -\; -->1)(-<!--\; -\; -->2)$
4. $a_n=-<!--\; -\; -->20+(n-<!--\; -\; -->1)+5$

5. A sequence is defined recursively by $f_1=3$, $f_n=2\cdot <!--\; \cdot \; -->f_{n-<!--\; -\; -->1}$, $n\ge <!--\; \ge \; -->2$. Which of the following gives the $n^{th}$ term for $n\ge <!--\; \ge \; -->0$?

1. $f_n=3+2^n$
2. $f_n=3+2n$
3. $f_n=3^n$
4. $f_n=3\cdot <!--\; \cdot \; -->2^{n-<!--\; -\; -->1}$

6. A sequence of numbers is given by $a_2=1$, $a_3=5$, $a_4=9$, $a_5=13$, $a_6=17$. Which expression can be used to find the $n^{th}$ term of the sequence?

1. $3n-<!--\; -\; -->4$
2. $7n-<!--\; -\; -->4$
3. $4n-<!--\; -\; -->7$
4. $4n-<!--\; -\; -->3$

7. A sequence of numbers is given by $\frac{1}{27}$, $\frac{1}{9}$, $\frac{1}{3}$, 1, …. What is the equation that can be used to find the $n^{th}$ term of the sequence?

1. $a_n=\frac{1}{27}÷<!--\; ÷\; -->3(n-<!--\; -\; -->1)$
2. $a_n=\frac{1}{27}(3{)}^{n-<!--\; -\; -->1}$
3. $a_n=\frac{1}{27}(\frac{1}{3}{)}^{n-<!--\; -\; -->1}$
4. $a_n=\frac{1}{27}-<!--\; -\; -->\frac{1}{3}(n-<!--\; -\; -->1)$

8. A sequence is given by the set of numbers 5, 1, -3, -7 … What is the equation that can be used to find the $n^{th}$ term of the sequence?

1. $a_n=5-<!--\; -\; -->(n-<!--\; -\; -->1)(-<!--\; -\; -->4)$
2. $a_n=5(4{)}^{n-<!--\; -\; -->1}$
3. $a_n=5(-<!--\; -\; -->4{)}^{n-<!--\; -\; -->1}$
4. $a_n=5+(n-<!--\; -\; -->1)(-<!--\; -\; -->4)$

9. A sequence consists of the following terms: 1280, 320, 80, … What is the explicit formula for this sequence?

1. $a_n=1280÷<!--\; ÷\; -->4(n-<!--\; -\; -->1)$
2. $a_n=1280(\frac{1}{4}{)}^{n-<!--\; -\; -->1}$
3. $a_n=1280(4{)}^{n-<!--\; -\; -->1}$
4. $a_n=1280-<!--\; -\; -->960(n-<!--\; -\; -->1)$

10. An arithmetic sequence consists of the terms 1, 6, 11, 16 …. If you were asked to find the ${100}^{th}$ term, what is the general formula you would use to find that value efficiently?

1. $a_n=1+5(a_{n-<!--\; -\; -->1})$
2. $a_n=5+a_{n-<!--\; -\; -->1}$
3. $a_n=1(a_{n-<!--\; -\; -->1}{)}^5$
4. $a_n=1+5(n-<!--\; -\; -->1)$