Question

Vocabulary words
Definition or Description


Lesson 2: Introduction to Sequences
arithmetic sequence




common difference


geometric sequence




common ratio


domain




range


function




sequence




index


notation




quadratic sequence




recursion




recursive formula


subscript




term




Lesson 3: Formulas for Sequences
explicit formula




Lesson 4: Arithmetic Sequences
coordinate grid




linear function




slope




term number




x-axis




y-axis


Lesson 5: Geometric Sequences
exponential function




Lesson 6: Linear Change
linear change




y-intercept




Lesson 7: Exponential growth
exponential equation




exponential growth




Lesson 8: Exponential Decay
exponential decay function




horizontal asymptote




initial amount




rate of decay

Answer 1

Below are concise definitions/descriptions for each vocabulary word, grouped by lesson.

Lesson 2: Introduction to Sequences
- arithmetic sequence: A sequence in which consecutive terms differ by the same constant. General form: a_n = a_1 + (n−1)d.
- common difference: The constant difference d between consecutive terms in an arithmetic sequence: d = a_{n+1} − a_n.
- geometric sequence: A sequence in which each term is obtained by multiplying the previous term by the same constant. General form: a_n = a_1·r^{\,n−1}.
- common ratio: The constant factor r between consecutive terms in a geometric sequence: r = a_{n+1}/a_n.
- domain: The set of allowable input values for a relation or function (often x-values).
- range: The set of possible output values of a relation or function (often y-values).
- function: A rule that assigns exactly one output to each input in its domain.
- sequence: An ordered list of numbers (a_1, a_2, a_3, …), often described by a rule for the nth term.
- index: The position number (usually n) used to identify a term in a sequence.
- notation: Symbols used to represent sequences and functions (e.g., a_n, f(x)).
- quadratic sequence: A sequence whose nth term is given by a quadratic expression in n (an^2 + bn + c); second differences are constant.
- recursion: Defining later terms of a sequence using previous terms.
- recursive formula: A formula that defines a_n in terms of earlier term(s), e.g., a_n = a_{n−1} + 3 with a_1 given.
- subscript: The small index written to the lower right of a symbol to indicate position (e.g., the “n” in a_n).
- term: A single element of a sequence (e.g., a_5 is the fifth term).

Lesson 3: Formulas for Sequences
- explicit formula: A formula that gives the nth term directly in terms of n (for example, a_n = 2n + 1 for an arithmetic sequence).

Lesson 4: Arithmetic Sequences
- coordinate grid: A two-dimensional plane with perpendicular axes used to locate points by ordered pairs (x, y).
- linear function: A function whose graph is a straight line; typically y = mx + b.
- slope: The rate of change of a line, rise over run: m = (change in y)/(change in x).
- term number: The index n that identifies which term in a sequence you are referring to (same as index).
- x-axis: The horizontal axis on a coordinate grid.
- y-axis: The vertical axis on a coordinate grid.

Lesson 5: Geometric Sequences
- exponential function: A function of the form f(x) = a·b^x where the variable is in the exponent; growth if b>1, decay if 0<b<1.

Lesson 6: Linear Change
- linear change: Change at a constant rate; modeled by linear functions.
- y-intercept: The value of y where a graph crosses the y-axis (the output when x = 0), commonly b in y = mx + b.

Lesson 7: Exponential growth
- exponential equation: An equation in which the variable appears in an exponent, e.g., 3·2^x = 24.
- exponential growth: A process that increases multiplicatively over equal increments (modeled by y = a·b^x with b > 1).

Lesson 8: Exponential Decay
- exponential decay function: An exponential function y = a·b^x with 0 < b < 1, representing quantities that decrease multiplicatively over time.
- horizontal asymptote: A horizontal line that a graph approaches as x → ∞ or x → −∞ (for many exponential models, y = 0 is an asymptote).
- initial amount: The value of the quantity at x = 0 in an exponential model; the coefficient a in y = a·b^x.
- rate of decay: The proportion lost each time unit; if b is the multiplier (0<b<1), the decay rate r = 1 − b (often expressed as a percent).

If you want, I can add a short example for any term or create flashcards/quiz questions.