Chapter 11

Write each repeating decimal as a fraction. \(0 . \overline{1}\)

Find the indicated term of each geometric sequence. $$ a_{6}=3, r=2, n=12 $$

Find the indicated term of each arithmetic sequence. \(a_{1}=35, d=3, n=101\)

Find \(a_{1}\) for each arithmetic series described. $$ d=-2, n=18, S_{18}=18 $$

Expand each power. $$ (3 x+2 y)^{4} $$

Find the first three iterates of each function for the given initial value. $$ f(x)=2 x^{2}-5, x_{0}=-1 $$

Write each repeating decimal as a fraction. \(0 . \overline{36}\)

Write an equation for the nth term of each geometric sequence. $$ 36,12,4, \dots $$

Write an equation for the \(n\) the term of each geometric sequence. $$ 36,12,4, \dots $$

Find the indicated term of each arithmetic sequence. \(a_{1}=20, d=4, n=81\)

Expand each power. $$ \left(\frac{a}{2}+2\right)^{5} $$

Find the first three iterates of each function for the given initial value. $$ f(x)=3 x^{2}-4, x_{0}=1 $$

Write each repeating decimal as a fraction. \(0 . \overline{82}\)

Find the sum of each geometric series. \(7+21+63+\dots\) to 10 terms

Write an equation for the nth term of each geometric sequence. $$ 64,16,4, \dots $$

Find the indicated term of each arithmetic sequence. \(a_{12}\) for \(-17,-13,-9, \ldots\)

ACT/SAT PQRS is a square. What is the ratio of the length of diagonal \(\overline{Q S}\) to the length of side \(\overline{R S}\) ? A 2 B \(\sqrt{2}\) C 1 D \(\frac{\sqrt{2}}{2}\)

Expand each power. $$ \left(3+\frac{m}{3}\right)^{5} $$

Find the first three iterates of each function for the given initial value. $$ f(x)=2 x^{2}+2 x+1, x_{0}=\frac{1}{2} $$

Find the sum of each geometric series. $$ \sum_{n=1}^{9} 5 \cdot 2^{n-1} $$

Write an equation for the nth term of each geometric sequence. $$ -2,10,-50, \dots $$

Find the indicated term of each arithmetic sequence. \(a_{12}\) for \(8,3,-2, \dots\)

Evaluate each expression. $$ \frac{12 !}{8 ! 4 !} $$

Find the sum of each geometric series. $$ \sum_{n=1}^{6} 2(-3)^{n-1} $$

Write an equation for the nth term of each geometric sequence. $$ 4,-12,36, \dots $$

To prove that objects of different weights fall at the same rate, Galileo dropped two objects with different weights from the Leaning Tower of Pisa in Italy. The objects hit the ground at the same time. When an object is dropped from a tall building, it falls about 16 feet in the first second, 48 feet in the second second, and 80 feet in the third second, regardless of its weight. How many feet would an object fall in the sixth second?

Expand each power. $$ (x+y)^{6} $$

Evaluate each expression. $$ \frac{14 !}{5 ! 9 !} $$

OPEN ENDED Write a recursive formula for a sequence whose first three terms are \(1,1, \) and \(3 .\)

In a physics experiment, a steel ball on a flat track is accelerated and then allowed to roll freely. After the first minute, the ball has rolled 120 feet. Each minute the ball travels only 40% as far as it did during the preceding minute. How far does the ball travel?

Find the geometric means in each sequence. \(9, ?, ?, 144\)

Geologists estimate that the continents of Europe and North America are drifting apart at a rate of an average of 12 miles every 1 million years, or about 0.75 inch per year. If the continents continue to drift apart at that rate, how many inches will they drift in 50 years? (Hint: \(a_{1}=0.75\))

Find the sum of each arithmetic series. $$ 6+13+20+27+\cdots+97 $$

Expand each power. $$ (a-b)^{7} $$

Find the indicated term of each expansion. fifth term of \((2 a+3 b)^{10}\)

REASONING Is the statement \(x_{n} \neq x_{n-1}\) sometimes, always, or never true if \(x_{n}=f\left(x_{n-1}\right) ?\) Explain.

Find the sum of each infinite geometric series, if it exists. \(\frac{5}{3}-\frac{10}{9}+\frac{20}{27}-\dots\)

Find the sum of each arithmetic series. $$ 7+14+21+28+\dots+98 $$

Expand each power. $$ (2 x+y)^{8} $$

Find the indicated term of each expansion. fourth term of \((2 x+3 y)^{9}\)

Find the sum of each infinite geometric series, if it exists. \(\frac{3}{2}-\frac{3}{4}+\frac{3}{8}-\dots\)

Find the indicated term for each geometric series described. $$ S_{n}=-364, r=-3, n=6 ; a_{1} $$

Complete the statement for each arithmetic sequence. 124 is the \(\underline{?}\) term of \(-2,5,12, \ldots\)

Find the first three iterates of each function for the given initial value. $$ f(x)=3 x-2, x_{0}=2 $$

Find the indicated term of each expansion. fourth term of \(\left(x+\frac{1}{3}\right)^{7}\)

Find the sum of each infinite geometric series, if it exists. \(3+1.8+1.08+\ldots\)

Find the indicated term for each geometric series described. $$ S_{n}=1530, r=2, n=8 ; a_{1} $$

Write an equation for the nth term of each arithmetic sequence. \(7,16,25,34, \dots\)

Find the sum of each arithmetic series. $$ 16+10+4+\cdots+(-50) $$

Find the first three iterates of each function for the given initial value. $$ f(x)=4 x^{2}-2, x_{0}=1 $$