Practice - Algebra 1

4.18.7 Practice

4.18.7 • Practice

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

Find the value of each specified term of the arithmetic sequences below.

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

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

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

Find the value of each specified term of the geometric sequences below.

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

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

A sequence is defined recursively by $f_1=-6, f_n=f_{n-1}-2$ , for $n≥2$ . Which of the following gives the $n^{th}$ term for $n≥0$ ?

$a_{n}=-6+(n)(-2)$
$a_{n}=-6+(n-1)+(-2)$
$a_{n}=-6+(n-1)(-2)$
$a_{n}=-2+(n-1)(-6)$

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

$a_{n}=5+(n-1)(-20)$
$a_{n}=-20+(n-1)(5)$
$a_{n}=-20+(n-1)(-2)$
$a_{n}=-20+(n-1)+5$

A sequence is defined recursively by $f_1=3$ , $f_n=2 \cdot f_{n-1}$ , $n\geq2$ . Which of the following gives the $n^{th}$ term for $n\geq0$ ?

$f_n=3+2^n$
$f_n=3+2n$
$f_n=3^n$
$f_n=3 \cdot 2^{n-1}$

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?

$3n-4$
$7n-4$
$4n-7$
$4n-3$

A sequence of numbers is given by $\frac{1}{27}$ , $\frac19$ , $\frac13$ , 1, …. What is the equation that can be used to find the $n^{th}$ term of the sequence?

$a_n = \frac{1}{27}\div3(n-1)$
$a_n = \frac{1}{27}(3)^{n-1}$
$a_n = \frac{1}{27}(\frac{1}{3})^{n-1}$
$a_n = \frac{1}{27}-\frac{1}{3}(n-1)$

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?

$a_n = 5 - (n-1)(-4)$
$a_n = 5(4)^{n-1}$
$a_n = 5(-4)^{n-1}$
$a_n = 5 + (n-1)(-4)$

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

$a_n = 1280 \div 4(n-1)$
$a_n = 1280 (\frac 14)^{n-1}$
$a_n = 1280 (4)^{n-1}$
$a_n = 1280 - 960(n-1)$

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?

$a_n = 1 + 5(a_{n-1})$
$a_n = 5+ a_{n-1}$
$a_n = 1 (a_{n-1})^5$
$a_n = 1 +5(n-1)$