MM250 DISCRETE MATH LAB Command Center

3. Sequences, Series, and Algorithms

VERIFIED AGAINST MM250 MATERIAL

Sections: 3.1 · 3.2 · 3.3 · 3.4 · 3.5 · 3.6 · 3.7

CALCULATORVERIFIED AGAINST MM250 MATERIAL

Sequence Generator / nth-Term Evaluator

§3.1 · Enter a general term a_n, generate the first N terms, or evaluate any specific term.

Generate first N terms

Evaluate a specific term

A sequence is a function whose domain is the positive integers. A finite sequence has a last term; an infinite sequence does not.
EVALUATORVERIFIED AGAINST MM250 MATERIAL

Arithmetic/Geometric Sequence Classifier

§3.3–3.4 · Enter terms to detect a common difference, common ratio, both, or neither.

REMEMBER: a constant sequence (every term the same) counts as both arithmetic (d=0) and geometric (r=1).
CALCULATORVERIFIED AGAINST MM250 MATERIAL

Arithmetic Sequence & Series Helper

§3.3 · a_n = a₁ + d(n−1) and S_n = (n/2)(a₁ + a_n).

REMEMBER: "Always use second form!!" — S_n = (n/2)(a₁ + a_n), not the alternate form built from d alone.
CALCULATORVERIFIED AGAINST MM250 MATERIAL

Geometric Sequence & Finite Series Helper

§3.4 · a_n = a₁r^(n−1) and S_n = a₁(1−r^n)/(1−r).

REMEMBER: "Always use FIRST form." — S_n = a₁(1−r^n)/(1−r). This tool automatically switches to S_n = a₁ × n when r = 1, since the first-form formula would divide by zero.
CALCULATORVERIFIED AGAINST MM250 MATERIAL

Infinite Geometric Series

§3.4 · Converges only when |r| < 1, giving S_∞ = a₁/(1−r).

REMEMBER: if |r| ≥ 1 (equivalently r ≤ −1 or r ≥ 1), the series has no finite sum — it diverges.
CALCULATORVERIFIED AGAINST MM250 MATERIAL

Sigma Notation / Summation Lab

§3.2, 3.7 · Expand and evaluate Σ (sigma) sums with a selectable starting index.

Σ (capital sigma) means summation: the expression to the right is the general term, the lower limit gives the first index, and the upper limit gives the last — both inclusive.
STEPPERVERIFIED AGAINST MM250 MATERIAL

Recurrence Relation Generator

§3.5 · Generate terms from a starting value a₀ using an arithmetic or geometric recurrence.

zyBooks indexes these recurrences starting at a₀, not a₁ — this tool follows that convention rather than assuming a₁ is always the start.
STEPPERVERIFIED AGAINST MM250 MATERIAL

Algorithm / Pseudocode Stepper

§3.6 · Trace variable values and control flow step-by-step through course-style pseudocode.

Supported constructs: assignment (x := expr), Return(expr), if (cond) then / else / endif, for v := start to end / endfor, while (cond) / endwhile — including nested loops. Conditions use <, >, <=, >=, ==, !=.
CALCULATORVERIFIED AGAINST MM250 MATERIAL

Arithmetic Mean

§3.1 · Simple average of a list of values.

This tool is seminar-supported rather than drawn from the Unit 3 zyBooks PDF specifically — the formula itself is basic and universal, but its course source is the instructor's seminar material, not the assigned reading reviewed in this pass.