Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58. If {a_n} is a finite sequence whose last term is -83, how many terms does {a_n} contain?

Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58. Find the difference between the sum of the first 14 terms of {b_n} and the sum of the first 14 terms of {a_n}.

In the sequence 21,700, 23,172, 24,644, 26,116,... which term is 314,628?

Show that the sum of the first n positive odd integers,1 +3 +5 + ··· + (2n − 1), ... is n².

Write an equation in point-slope form and slope-intercept form for the line passing through (-2, -6) and perpendicular to the line whose equation is x − 3y+ 9 = 0.

Solve: log₂ (x+9) — log₂ x = 1.

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

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

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

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

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 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 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 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 = 1 000 000, r = 0.1

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a_n to find a₇, the seventh term of the sequence. 3, 12, 48, 192, ...

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a_n to find a₇, the seventh term of the sequence. 18, 6, 2, 2/3, ...

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a_n to find a₇, the seventh term of the sequence. 1.5, - 3, 6, -12, ...

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a_n to find a₇, the seventh term of the sequence. 0.0004, - 0.0004, 0.04, - 0.04, ...

Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises 25–30. Find the sum of the first 12 terms of the geometric sequence: 2, 6, 18, 54, ...

Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises 25–30. Find the sum of the first 11 terms of the geometric sequence: 3, - 6, 12, - 24, ...

Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises 25–30. Find the sum of the first 14 terms of the geometric sequence: - 3/2, 3, - 6, 12, ...

Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.${\sum }_{i=1}^8{3}^i$

Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. ${\sum }_{i=1}^{10}5\cdot 2^i$

Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.${\sum }_{i=1}^6{\left(\frac{1}{2}\right)}^{i+1}$

Find the sum of each infinite geometric series. 1 + 1/3 + 1/9 + 1/27 + ...

Find the sum of each infinite geometric series. 3 + 3/4 + 3/4² + 3/4³ + ...

Find the sum of each infinite geometric series. 1 - 1/2 + 1/4 - 1/8 + ...

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

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