Public learning track
Arithmetic Sequences and Series
10th Grade · Math · Open Global Math
6 lessons
Goal
Derive explicit and recursive formulas for arithmetic sequences, calculate partial sums using sigma notation, and model linear progression phenomena.
Featured Diagrams
Identifying Arithmetic Sequences and the Common Difference
6 lessons
0 of 6 done
- 1Identifying Arithmetic Sequences and the Common DifferenceUp nextStart
- 2Deriving the nth-Term Formula of an Arithmetic SequencePremiumNot started yet
- 3Finding Initial Terms and Differences from Given TermsNot started yet
- 4Deriving and Applying the Arithmetic Series Sum FormulaNot started yet
- 5Finding Sums of Arithmetic Series in Sigma NotationNot started yet
- 6Modeling Real-World Situations with Arithmetic Sequences and SeriesNot started yet
Curriculum Framework
10th Grade · Math · Open Global Math
1
8 lessons
Real Number Foundations, Density, and Decimal Expansions
Analyze the structural properties of real numbers, prove irrationality, explore set density, and convert recurring decimal expansions into exact rational forms.
2
5 lessons
Indices, Fractional Powers, and Radical Equivalences
Master integer and fractional exponent laws, convert between radical and exponential notation, and evaluate algebraic expressions with rational exponents.
3
7 lessons
Surds and Exact Radical Calculations
Simplify surds, perform arithmetic operations with radical expressions, expand binomial surds, and rationalize single and binomial denominators.
4
5 lessons
Scientific Notation, Significant Figures, and Order of Magnitude
Perform multi-step arithmetic operations with numbers in scientific notation and solve real-world scientific and astronomical scale problems.
5
5 lessons
Upper and Lower Bounds, Accuracy, and Error Intervals
Calculate bounds of rounded numbers and determine error propagation across multi-step arithmetic, geometric, and physical calculations.
6
7 lessons
Advanced Ratios, Proportionality, and Compound Units
Solve complex multi-part ratio problems, model direct and inverse proportion algebraically, and compute compound measures involving speed, density, and pressure.
7
7 lessons
Percentage Change, Compound Interest, and Depreciation
Solve multi-step percentage change and reverse percentage problems, and model compound growth and depreciation over varying compounding intervals.
8
5 lessons
Annuities, Loan Amortization, and Progressive Taxation
Analyze ordinary annuities, calculate regular payments and future values of sinking funds, model loan repayments, and compute progressive income taxes.
9
6 lessons
Arithmetic Sequences and Series
Derive explicit and recursive formulas for arithmetic sequences, calculate partial sums using sigma notation, and model linear progression phenomena.
10
7 lessons
Geometric Sequences and Infinite Series
Formulate explicit terms of geometric progressions, evaluate finite and infinite geometric series, and model exponential growth and annuity structures.
11
6 lessons
Quadratic and Non-Linear Sequences
Analyze sequence difference patterns, derive nth-term quadratic formulas, and explore cubic, geometric, and recursive sequence models.