Chapter 11

Evaluate the finite series for the specified number of terms. $$ 1+2+4+\ldots ; n=8 $$

Given each set of axes, what does the area under the curve represent? \(y\) -axis: production rate, \(x\) -axis: time

Write the related series for each finite sequence. Then evaluate each series. $$ 21,18,15,12,9,6,3 $$

Is the sequence geometric? If so, find the common ratio and the next two terms. $$ 1,2,4,8, \ldots $$

Describe each pattern formed. Find the next three terms. $$ 80,77,74,71,68, \dots $$

Evaluate the finite series for the specified number of terms. $$ 4+12+36+\ldots ; n=6 $$

Write the related series for each finite sequence. Then evaluate each series. $$ -5,-15,-25,-35,-45 $$

Is the sequence geometric? If so, find the common ratio and the next two terms. $$ 1,2,3,4, \dots $$

Is the given sequence arithmetic? If so, identify the common difference. \(10,20,30,40, \ldots\)

Describe each pattern formed. Find the next three terms. $$ 4,8,16,32,64, \dots $$

Given each set of axes, what does the area under the curve represent? y-axis: rate of growth, \(x\) -axis: time

Evaluate the finite series for the specified number of terms. $$ 3+6+12+\ldots ; n=7 $$

Write the related series for each finite sequence. Then evaluate each series. $$ 100,99,98, \dots, 95 $$

Is the sequence geometric? If so, find the common ratio and the next two terms. $$ 1,-2,4,-8, \dots $$

Is the given sequence arithmetic? If so, identify the common difference. \(1,1,2,3,5,8, \dots\)

Describe each pattern formed. Find the next three terms. $$ 0,3,7,12,18, \dots $$

Given each set of axes, what does the area under the curve represent? \(y\) -axis: distance traveled per year, \(x\) -axis: years

Evaluate the finite series for the specified number of terms. $$ 7-35+175-\ldots ; n=5 $$

Write the related series for each finite sequence. Then evaluate each series. $$ 0.5,0.25,0, \ldots,-0.75 $$

Is the sequence geometric? If so, find the common ratio and the next two terms. $$ -1,1,-1,1, \ldots $$

Describe each pattern formed. Find the next three terms. $$ 1,4,7,10,13, \dots $$

Given each set of axes, what does the area under the curve represent? \(y\) -axis: price per pound of gold, \(x\) -axis: pounds of gold

Is the sequence geometric? If so, find the common ratio and the next two terms. $$ 10,4,1.6,0.64, \dots $$

Is the given sequence arithmetic? If so, identify the common difference. \(-21,-18,-15,-12, \dots\)

Describe each pattern formed. Find the next three terms. $$ 100,10,1,0.1,0.01, \dots $$

Evaluate the finite series for the specified number of terms. $$ -\frac{1}{6}+1-6+36-\ldots ; n=5 $$

Write the related series for each finite sequence. Then evaluate each series. $$ 4.5,5.6,6.7, \ldots, 11.1 $$

Is the sequence geometric? If so, find the common ratio and the next two terms. $$ 7,0.7,0.07,0.007, \ldots $$

Is the given sequence arithmetic? If so, identify the common difference. \(97,86,75,64, \dots\)

Describe each pattern formed. Find the next three terms. $$ \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \dots $$

Evaluate the finite series for the specified number of terms. $$ \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\ldots ; n=8 $$

Each sequence has eight terms. Evaluate each related series. $$ \frac{1}{2}, \frac{3}{2}, \frac{5}{2}, \ldots, \frac{15}{2} $$

Is the sequence geometric? If so, find the common ratio and the next two terms. $$ 18,-6,2,-\frac{2}{3}, \dots $$

Is the given sequence arithmetic? If so, identify the common difference. \(3,7,11,15, \dots\)

Describe each pattern formed. Find the next three terms. $$ 4,-8,16,-32,64, \ldots $$

Evaluate the finite series for the specified number of terms. $$ 1-3+9-27+\ldots ; n=8 $$

Is the sequence geometric? If so, find the common ratio and the next two terms. $$ 1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \dots $$

Is the given sequence arithmetic? If so, identify the common difference. \(100,10,1,0.1, \ldots\)

Describe each pattern formed. Find the next three terms. $$ 1,2,6,24,120, \dots $$

Write and evaluate a sum to estimate the area under each curve for the domain \(0 \leq x \leq 2\) . a. Use inscribed rectangles 1 unit wide. b. Use eircumscribed rectangles 1 unit wide. $$ f(x)=\frac{1}{2} x^{2} $$

Decide whether each infinite geometric series diverges or converges. State whether each series has a sum. $$ 1+\frac{1}{4}+\frac{1}{16}+\ldots $$

Each sequence has eight terms. Evaluate each related series. $$ 5,13,21, \ldots, 61 $$

Is the sequence geometric? If so, find the common ratio and the next two terms. $$ 10,15,22.5,33.75, \dots $$

Is the given sequence arithmetic? If so, identify the common difference. \(\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \dots\)

Describe each pattern formed. Find the next three terms. $$ 0,1,0, \frac{1}{3}, 0, \frac{1}{5}, \dots $$

Write and evaluate a sum to estimate the area under each curve for the domain \(0 \leq x \leq 2\) . a. Use inscribed rectangles 1 unit wide. b. Use eircumscribed rectangles 1 unit wide. $$ y=-x^{2}+5 $$

Decide whether each infinite geometric series diverges or converges. State $$ 1-\frac{1}{2}+\frac{1}{4} $$

Is the sequence geometric? If so, find the common ratio and the next two terms. $$ 2,-10,50,-250, \dots $$

Is the given sequence arithmetic? If so, identify the common difference. \(-5,5,-5,5,-5, \dots\)

Write and evaluate a sum to estimate the area under each curve for the domain \(0 \leq x \leq 2\) . a. Use inscribed rectangles 1 unit wide. b. Use eircumscribed rectangles 1 unit wide. $$ g(x)=x^{2}+1 $$