Express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. a+ar+ar²+⋯+ ar¹²

Use a calculator's factorial key to evaluate each expression. (300/20)!

Use a calculator's factorial key to evaluate each expression. 20!/(20−3)!

Solve: x/(x−3)=2x/(x−3)−5/3

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

Write the first six terms of each arithmetic sequence.

$a_1=-8,d=5$

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

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

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

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

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

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

Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a₅₀ when a₁ = 7, d = 5.

Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a₂₀₀ when a₁ = −40, d = 5.

Find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a₆₀ when a₁ = 35, d = -3.

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. 1, 5, 9, 13,...

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. 7,3,-1,-5,...

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. a₁ = 9, d=2

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. a₁=-20, d = -4

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. a_n = a_n-1 +3, a₁ = 4

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. a_n= a_n-1 -10, a₁ = 30

Find the sum of the first 20 terms of the arithmetic sequence: 4, 10, 16, 22,……….

Find the sum of the first 50 terms of the arithmetic sequence: -10, -6, -2, 2,....

Find 1+2+3+4+...+ 100, the sum of the first 100 natural numbers.

Find the sum of the first 60 positive even integers.

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

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.

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

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.

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

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

Find a₁₄+b₁₂.