In Exercises 5–10, a statement Sn about the positive integers is given. Write statements S_k and S_k+1 simplifying statement S_k+1 completely. Sn: 2 is a factor of n² - n + 2.

Use the formula for nCr to evaluate each expression. ₉C₅

Write the first six terms of each arithmetic sequence. a_n = a_n-1 +6, a₁ = −9

Write the first four terms of each sequence whose general term is given. a_n=2n/(n+4)

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a₁ and common ratio, r. Find a₈ when a₁ = 6, r = 2

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (x+2)³

In Exercises 10–11, express each sum using summation notation. Use i for the index of summation. 1/3 + 2/4 + 3/5 + ... + 15/17

Use the formula for nCr to evaluate each expression. ₁₀C₆

Use mathematical induction to prove that each statement is true for every positive integer n. 4 + 8 + 12 + ... + 4n = 2n(n + 1)

In Exercises 11–16, a die is rolled. Find the probability of getting a 4.

In Exercises 1–12, write the first four terms of each sequence whose general term is given. a_n=(−1)ⁿ⁺¹/(2ⁿ−1)

Write the first six terms of each arithmetic sequence. a_n = a_n-1 -10, a₁ = 30

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a₁ and common ratio, r. Find a₁₂ when a₁ = 5, r = - 2

Use the formula for nCr to evaluate each expression. ₁₁C₄

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $(3x+y{)}^3$

Write the first six terms of each arithmetic sequence. a_n = a_n-1 -0.4, a₁ = 1.6

Use mathematical induction to prove that each statement is true for every positive integer n. 1 + 3 + 5 + ... + (2n - 1) = n²

In Exercises 11–16, a die is rolled. Find the probability of getting an odd number.

Use the formula for nCr to evaluate each expression. ₇C₇

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a₁ and common ratio, r. Find a₄₀ when a₁ = 1000, r = - 1/2

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $(5x\text{–}1{)}^3$

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a₁=7 and a_n=a_n-1 + 5 for n≥2

In Exercises 12–15, write the first six terms of each arithmetic sequence. a1 = 3/2, d = -1/2

Use the formula for _nC_r to evaluate each expression. ₄C₄

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $(2x+1{)}^4$

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a₁=3 and a_n=4a_n-1 for n≥2

In Exercises 11–16, a die is rolled. Find the probability of getting a number greater than 4.

Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a₆ when a₁ = 13, d = 4.

Use mathematical induction to prove that each statement is true for every positive integer n. 3 + 7 + 11 + ... + (4n - 1) = n(2n + 1)

Use the formula for nCr to evaluate each expression. ₅C₀