Write the first six terms of each arithmetic sequence. a₁ = 200, d = 20

Use the formula for _nP_r to evaluate each expression. ₉P₄

Write the first four terms of each sequence whose general term is given. a_n = 7n - 4

Write the first four terms of each sequence whose general term is given. a_n=3n+2

Write the first five terms of each geometric sequence. a₁ = 5, r = 3

Evaluate the given binomial coefficient.$\left(\frac{8}{3}\right)$

A statement S_n about the positive integers is given. Write statements S₁, S₂ and S₃ and show that each of these statements is true. S_n: 1 + 3 + 5 + ... + (2n - 1) = n²

A statement S_n about the positive integers is given. Write statements S₁, S₂ and S₃ and show that each of these statements is true. S_n: 3 + 4 + 5 + ... + (n + 2) = n(n + 5)/2

Write the first four terms of each sequence whose general term is given. $a_n=1/(n-1)!$

Write the first four terms of each sequence whose general term is given. a_n=3ⁿ

Use the formula for _nP_r to evaluate each expression. ₈P₅

Evaluate the given binomial coefficient. $\left(\frac{12}{1}\right)$

Write the first five terms of each geometric sequence. a₁ = 20, r = 1/2

Use the formula for _nP_r to evaluate each expression. ₁₀P₄

Write the first six terms of each arithmetic sequence.

$a_1=-8,d=5$

A statement S_n about the positive integers is given. Write statements S₁, S₂ and S₃ and show that each of these statements is true. S_n: 3 is a factor of n³ - n.

A statement S_n about the positive integers is given. Write statements S_k and S_k+1 simplifying statement S_k+1 completely. Sn: 4 + 8 + 12 + ... + 4n = 2n(n + 1)

Write the first six terms of each arithmetic sequence. a₁ = 300, d= -90

Write the first four terms of each sequence whose general term is given. a_n=(−3)ⁿ

Write the first five terms of each geometric sequence. a_n = - 4a_(n-1), a₁ = 10

Use the formula for nPr to evaluate each expression. ₆P₆

Evaluate the given binomial coefficient. $\left(\frac{6}{6}\right)$

A statement Sn about the positive integers is given. Write statements S_k and S_k+1 simplifying statement S_k+1 completely. Sn: 3 + 7 + 11 + ... + (4n - 1) = n(2n + 1)

Evaluate the given binomial coefficient. $\left(\frac{100}{2}\right)$

Evaluate $\frac{40!}{4!38!}$

Use the formula for nPr to evaluate each expression. ₈P₀

Write the first six terms of each arithmetic sequence. a₁= 5/2, d = -1/2

Write the first four terms of each sequence whose general term is given. a_n=(−1)ⁿ(n+3)

Write the first five terms of each geometric sequence. a_n = - 5a_(n-1), a₁ = - 6

In Exercises 8–9, find each indicated sum. This is a summation, refer to the textbook.