Find the sum of the first 15 terms of the geometric sequence: 5, -15, 45, -135

Find the sum of each infinite geometric series. ${\sum }_{i=1}^{\infty }8(-0.3{)}^{i-1}$

Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. $1^2+2^2+3^2+\cdots +{15}^2$

Find the term indicated in each expansion. (x² + y³)⁸; sixth term

Use the formula for the sum of the first n terms of a geometric sequence to find the indicated sum.

${\sum }_{i=1}^6{5}^i$

Find the sum of the even integers between 21 and 45.

Find the sum of the odd integers between 30 and 54.

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

${\sum }_{i=1}^{17}(5i+3)$

In Exercises 45-46, it is equally probable that the pointer on the spinner shown will land on any one of the eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again. Find the probability that the pointer will stop on an odd number or a number less than 6.

Express each repeating decimal as a fraction in lowest terms. $0.\bar{5}=\frac{5}{10}+\frac{5}{100}+\frac{5}{1000}+\frac{5}{10,000}+\cdots$

Express each sum using summation notation. Use $1$ as the lower limit of summation and $i$ for the index of summation. $2+2^2+2^3+\cdots +2^{11}$

Find the term indicated in each expansion. (x − 1/2)⁹; fourth term

Find the term indicated in each expansion. (x² + y)²²; the term containing y¹⁴

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

${\sum }_{i=1}^{30}(-3i+5)$

Find the sum of each infinite geometric series. 2 - 1 + 1/2 - 1/4 + ...

Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+2+3+⋯+ 30

Express each repeating decimal as a fraction in lowest terms. $0.\overline{47}=\frac{47}{100}+\frac{47}{10,000}+\frac{47}{1,000,000}+\cdots$

Find the sum of each infinite geometric series. -6 + 4 - 8/3 + 16/9 - ...

Express each repeating decimal as a fraction in lowest terms. $0.\overline{257}$

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

${\sum }_{i=1}^{100}4i$

Use the formula for nCr to solve Exercises 49–56. An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1/2+2/3+3/4+⋯+ 14/(14+1)

In Exercises 49–52, a single die is rolled twice. Find the probability of rolling a 2 the first time and a 3 the second time.

Use the Binomial Theorem to expand each expression and write the result in simplified form. (x³ +x^-2)⁴

Express each repeating decimal as a fraction in lowest terms. 0.6 (repeating 6)

Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58.

Find a₁₄+b₁₂.

Express each sum using summation notation. Use $1$ as the lower limit of summation and $i$ for the index of summation. $4+4^2/2+4^3/3+\cdots +4^n/n$

In Exercises 49–52, a single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 2 the second time.

The general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. a_n = n + 5

Use the formula for nCr to solve Exercises 49–56. Of 12 possible books, you plan to take 4 with you on vacation. How many different collections of 4 books can you take?