Chapter 11

Evaluate each infinite geometric series. $$ 1.1+0.11+0.011+\ldots $$

Find the area under each curve for the domain \(0 \leq x \leq 1\) $$ y=x^{3} $$

For each sum, find the number of terms, the first term, and the last term. Then evaluate the series. $$ \sum_{n=1}^{5}(-2 n-1) $$

Write the explicit formula for each sequence. Then generate the first five terms. $$ a_{1}=4, r=0.1 $$

Find the 32nd term of each sequence. \(13,17,21,25, \dots\)

Write an explicit formula for each sequence. Then find \(a_{12}\) $$ 4,7,10,13,16, \dots $$

Evaluate each infinite geometric series. $$ 1.1-0.11+0.011-\ldots $$

Find the area under each curve for the domain \(0 \leq x \leq 1\) $$ y=-x^{4}+2 x^{3}+3 $$

For each sum, find the number of terms, the first term, and the last term. Then evaluate the series. $$ \sum_{n=3}^{8}(7-n) $$

Write the explicit formula for each sequence. Then generate the first five terms. $$ a_{1}=10, r=-1 $$

Find the missing term of each arithmetic sequence. \(-16,\) _\(, 1, \ldots\)

Write an explicit formula for each sequence. Then find \(a_{12}\) $$ 3,7,11,15,19, \ldots $$

Evaluate each infinite geometric series. $$ 3+1+\frac{1}{3}+\frac{1}{9}+\ldots $$

Find the area under each curve for the domain \(0 \leq x \leq 1\) $$ y=x^{5}-x^{2}+2.5 $$

For each sum, find the number of terms, the first term, and the last term. Then evaluate the series. $$ \sum_{n=1}^{5}(0.2 n-0.2) $$

Find the missing term of each geometric sequence. It could be the geometric mean or its opposite. $$ 5, \square, 911.25, \dots $$

Find the missing term of each arithmetic sequence. \(14, \square, 28, \ldots\)

Write an explicit formula for each sequence. Then find \(a_{12}\) $$ -2 \frac{1}{2},-2,-1 \frac{1}{2},-1, \ldots $$

Evaluate each infinite geometric series. $$ 3+2+\frac{4}{3}+\frac{8}{9}+\dots $$

Find the area under each curve for the domain \(0 \leq x \leq 1\) $$ y=-(x-1)^{3}+3 $$

For each sum, find the number of terms, the first term, and the last term. Then evaluate the series. $$ \sum_{n=2}^{10} \frac{4 n}{3} $$

Find the missing term of each geometric sequence. It could be the geometric mean or its opposite. $$ 9180, \square, 255, \dots $$

Write an explicit formula for each sequence. Then find \(a_{12}\) $$ 2,5,10,17,26, \dots $$

Evaluate each infinite geometric series. $$ 3-2+\frac{4}{3}-\frac{8}{9}+\dots $$

Graph each curve. Use inscribed rectangles to approximate the area under the curve for the interval and rectangle width given. $$ y=x^{2}+1,1 \leq x \leq 3,0.5 $$

For each sum, find the number of terms, the first term, and the last term. Then evaluate the series. $$ \sum_{n=5}^{10}(20-n) $$

Find the missing term of each geometric sequence. It could be the geometric mean or its opposite. $$ \frac{2}{5}, \square, \frac{8}{45}, \dots $$

Find the missing term of each arithmetic sequence. \(\frac{13}{2}, \square, \frac{51}{2}, \ldots\)

Decide whether each formula is explicit or recursive. Then find the first five terms of each sequence. $$ a_{n}=2 a_{n-1}+3, \text { where } a_{1}=3 $$

Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified number of terms. \(2+4+8+16+\ldots ; n=10\)

Graph each curve. Use inscribed rectangles to approximate the area under the curve for the interval and rectangle width given. $$ y=3 x^{2}+2,2 \leq x \leq 4,1 $$

Tell whether each list is a sequence or a series. Then tell whether it is finite or infinite. $$ 1,2,4,8,16,32, \dots $$

Find the missing term of each geometric sequence. It could be the geometric mean or its opposite. $$ 3, \square, 0.75, \dots $$

Decide whether each formula is explicit or recursive. Then find the first five terms of each sequence. $$ a_{n}=\frac{1}{2}(n)(n-1) $$

Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified number of terms. \(2+4+6+8+\ldots ; n=20\)

Graph each curve. Use inscribed rectangles to approximate the area under the curve for the interval and rectangle width given. $$ y=x^{2}, 3 \leq x \leq 5,0.5 $$

Tell whether each list is a sequence or a series. Then tell whether it is finite or infinite. $$ 1,0.5,0.25,0.125,0.0625 $$

Find the missing term of each geometric sequence. It could be the geometric mean or its opposite. $$ 5, \square, 2.8125, \dots $$

Find the missing term of each arithmetic sequence. \(203, \square, 1117, \ldots\)

Decide whether each formula is explicit or recursive. Then find the first five terms of each sequence. $$ (n-5)(n+5)=a_{n} $$

Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified number of terms. \(6.4+8+10+12.5+\ldots .; n=7\)

Graph each curve. Use inscribed rectangles to approximate the area under the curve for the interval and rectangle width given. $$ y=2 x^{2}, 3 \leq x \leq 5,1 $$

Find the missing term of each geometric sequence. It could be the geometric mean or its opposite. $$ 12, \square, 3, \dots $$

Decide whether each formula is explicit or recursive. Then find the first five terms of each sequence. $$ a_{n}=-3 a_{n-1}, \text { where } a_{1}=-2 $$

Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified number of terms. \(-5+25-125+625-\ldots ; n=9\)

Graph each curve. Use inscribed rectangles to approximate the area under the curve for the interval and rectangle width given. $$ y=x^{3}, 1 \leq x \leq 3,0.25 $$

Tell whether each list is a sequence or a series. Then tell whether it is finite or infinite. $$ -0.5-0.25-0.125-\ldots $$

Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. $$ 45,90,180,360, \dots $$

Find the missing term of each arithmetic sequence. \(.65, \square,-60, \dots\)

Decide whether each formula is explicit or recursive. Then find the first five terms of each sequence. $$ a_{n}=-4 n^{2}-2 $$