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0. Review of Algebra(0)

Algebraic Expressions
(0)

Exponents
(0)

Polynomials Intro
(0)

Multiplying Polynomials
(0)

Factoring Polynomials
(0)

Radical Expressions
(0)

Simplifying Radical Expressions
(0)

Rationalize Denominator
(0)

Rational Exponents
(0)

1. Equations & Inequalities(0)

Linear Equations
(0)

Rational Equations
(0)

The Imaginary Unit
(0)

Powers of i
(0)

Complex Numbers
(0)

Intro to Quadratic Equations
(0)

The Square Root Property
(0)

Completing the Square
(0)

The Quadratic Formula
(0)

Choosing a Method to Solve Quadratics
(0)

Linear Inequalities
(0)

2. Graphs of Equations(0)

Graphs and Coordinates
(0)

Two-Variable Equations
(0)

Lines
(0)

3. Functions(0)

Intro to Functions & Their Graphs
(0)

Common Functions
(0)

Transformations
(0)

Function Operations
(0)

Function Composition
(0)

4. Polynomial Functions(0)

Quadratic Functions
(0)

Understanding Polynomial Functions
(0)

Graphing Polynomial Functions
(0)

Dividing Polynomials
(0)

Zeros of Polynomial Functions
(0)

5. Rational Functions(0)

Introduction to Rational Functions
(0)

Asymptotes
(0)

Graphing Rational Functions
(0)

6. Exponential & Logarithmic Functions(0)

Introduction to Exponential Functions
(0)

Graphing Exponential Functions
(0)

The Number e
(0)

Introduction to Logarithms
(0)

Graphing Logarithmic Functions
(0)

Properties of Logarithms
(0)

Solving Exponential and Logarithmic Equations
(0)

7. Systems of Equations & Matrices(0)

Two Variable Systems of Linear Equations
(0)

Introduction to Matrices
(0)

Determinants and Cramer's Rule
(0)

Graphing Systems of Inequalities
(0)

8. Conic Sections(0)

Introduction to Conic Sections
(0)

Circles
(0)

Ellipses: Standard Form
(0)

Parabolas
(0)

Hyperbolas at the Origin
(0)

Hyperbolas NOT at the Origin
(0)

9. Sequences, Series, & Induction(0)

Sequences
(0)

Arithmetic Sequences
(0)

Geometric Sequences
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10. Combinatorics & Probability(0)

Factorials
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Combinatorics
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Probability
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9. Sequences, Series, & Induction

Geometric Sequences

9. Sequences, Series, & Induction

Geometric Sequences: Video e Problemi di Pratica

Videolezioni Pratica Foglio di lavoro

53 problemi

Tipi di problemi che vuoi esercitarti:

Problema 1Scelta multipla

Find the sixth term of the sequence 17, 68, 272, 1088,... using the equation a_n = a₁(4)^n-1

Problema 2Scelta multipla

Using the equation of the nth term of the sequence, evaluate a₂/a₁, a₃/a₂, a₄/a₃ and a₅/a₄: a_n = 5(7)ⁿ.

What do you notice?

Problema 3Scelta multipla

For the following sequence, evaluate a₂/a₁, a₃/a₂, a₄/a₃ and a₅/a₄: 9, -27, 81, -243, 729,...

What do you notice?

Problema 4Scelta multipla

Determine the missing terms in the given geometric sequence.

81, a₂, a₃, -24

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Problema 5Scelta multipla

Determine the missing terms in the given geometric sequence.

64, a₂, a₃, 125

Problema 6Scelta multipla

Two unique sequences are given below.

{a_n} = -3, 6, -12, 24, ...,

{b_n} = 4, -6, -16, -26, ...,

What is the difference between the sum of the first 12 terms of {a_n} and {b_n}?

Problema 7Scelta multipla

Two unique sequences are given below.

{a_n} = -3, 6, -12, 24, ...,

{b_n} = 4, -6, -16, -26, ...,

What is a₈ + b₈?

comments

Problema 8Scelta multipla

Identify if the following sequence is arithmetic, geometric, or none of them. In the case of an arithmetic sequence, determine its common difference, and in the case of a geometric sequence, determine its common ratio.

a_n = n³ + 1

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Problema 9Scelta multipla

a_n = 7ⁿ

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Problema 10Scelta multipla

a_n = 2 + n

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Problema 11Scelta multipla

Rewrite and simplify the given recurring decimal as a fraction.

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Problema 12Scelta multipla

Rewrite and simplify the given recurring decimal as a fraction.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mn>0</mn><mo>.</mo><mover><mn>39</mn><mo>¯</mo></mover><mo>=</mo><mfrac><mn>39</mn><mn>100</mn></mfrac><mo>+</mo><mfrac><mn>39</mn><mn>10000</mn></mfrac><mo>+</mo><mfrac><mn>39</mn><mn>1000000</mn></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo></mstyle></math>","truncated":false}$

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Problema 13Scelta multipla

Rewrite and simplify the given recurring decimal as a whole number.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mn>0</mn><mo>.</mo><mover><mn>9</mn><mo>¯</mo></mover><mo>=</mo><mfrac><mn>9</mn><mn>10</mn></mfrac><mo>+</mo><mfrac><mn>9</mn><mn>100</mn></mfrac><mo>+</mo><mfrac><mn>9</mn><mn>1000</mn></mfrac><mo>+</mo><mfrac><mn>9</mn><mn>10000</mn></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo></mstyle></math>","truncated":false}$

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Problema 14Scelta multipla

For the given infinite series, evaluate the sum.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mo>∞</mo></munderover><mn>6</mn><msup><mrow><mo>(</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>4</mn><mo>)</mo></mrow><mrow><mi>j</mi><mo>-</mo><mn>1</mn></mrow></msup></mstyle></math>","truncated":false}$

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Problema 15Scelta multipla

For the given infinite series, evaluate the sum.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mn>5</mn><mo>+</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>5</mn><msup><mn>2</mn><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>5</mn><msup><mn>2</mn><mn>3</mn></msup></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo></mstyle></math>","truncated":false}$

Problema 16Scelta multipla

For the given infinite series, evaluate the sum.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mn>1</mn><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>+</mo><mfrac><mn>1</mn><mn>25</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>125</mn></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo></mstyle></math>","truncated":false}$

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Problema 17Scelta multipla

For the given infinite series, evaluate the sum.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>+</mo><mfrac><mn>1</mn><mn>16</mn></mfrac><mo>+</mo><mfrac><mn>1</mn><mn>64</mn></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo></mstyle></math>","truncated":false}$

Problema 18Scelta multipla

Evaluate the specified sum for the given geometric sequence.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mn>7</mn></munderover><msup><mfenced><mfrac><mn>1</mn><mn>3</mn></mfrac></mfenced><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msup></mstyle></math>","truncated":false}$

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Problema 19Scelta multipla

Evaluate the specified sum for the given geometric sequence.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mn>12</mn></munderover><mn>4</mn><mo>·</mo><msup><mn>5</mn><mi>k</mi></msup></mstyle></math>","truncated":false}$

Problema 20Scelta multipla

Evaluate the specified sum for the given geometric sequence.

${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>10</mn></munderover><msup><mn>2</mn><mi>i</mi></msup></mstyle></math>","truncated":false}$

Problema 21Scelta multipla

Evaluate the sum of the first 10 terms for the geometric sequence given below

36, 6, 1, 1/6, 1/36,...

Problema 22Scelta multipla

Evaluate the sum of the first 8 terms for the geometric sequence given below.

5, -7.5, 11.25, -16.875,...

Problema 23Scelta multipla

Evaluate the sum of the first 11 terms for the geometric sequence given below.

4, -10, 25, -125/2,...

Problema 24Scelta multipla

Work out the formula for the n^th term of the given geometric sequence, and find the eighth term (a₈) using the formula we came up with.

0.0000003, -0.00003, 0.003,....

Problema 25Scelta multipla

Work out the formula for the n^th term of the given geometric sequence, and find the eighth term (a₈) using the formula we came up with.

3, -9, 27, -81,...

Problema 26Scelta multipla

Work out the formula for the n^th term of the given geometric sequence, and find the eighth term (a₈) using the formula we came up with.

56, 14, 3.5, 0.875,...

Problema 27Scelta multipla

Work out the formula for the n^th term of the given geometric sequence, and find the eighth term (a₈) using the formula we came up with.

64, 96, 144, 216,...

Problema 28Scelta multipla

The first term (a₁) and the common ratio (r) of a geometric sequence are given. Find the specified term using the general term (n^th term) formula.

Find a₁₂ when a₁ = 200 000 000, r = 0.2.

Problema 29Scelta multipla

The first term (a₁) and the common ratio (r) of a geometric sequence are given. Find the specified term using the general term (n^th term) formula.

Find a₂₅ when a₁ = 6000, r = -1/3.

Problema 30Scelta multipla

The first term (a₁) and the common ratio (r) of a geometric sequence are given. Find the specified term using the general term (n^th term) formula.

Find a₁₅ when a₁ = 4, r = -3.

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Geometric Sequences: Video e Problemi di Pratica

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