SL 1.1—Using standard form

SL 1.2—Arithmetic sequences and series

SL 1.3—Geometric sequences and series

SL 1.4—Financial apps – compound interest, annual depreciation

SL 1.5—Intro to logs

SL 1.6—Simple proof

SL 1.7—Laws of exponents and logs

SL 1.8—Sum of infinite geo sequence

SL 1.9—Binomial theorem where n is an integer

AHL 1.10—Perms and combs, binomial with negative and fractional indices

AHL 1.11—Partial fractions

AHL 1.12—Complex numbers – Cartesian form and Argand diag

AHL 1.13—Polar and Euler form

AHL 1.14—Complex roots of polynomials, conjugate roots, De Moivre’s, powers & roots of complex numbers

AHL 1.15—Proof by induction, contradiction, counterexamples

AHL 1.16—Solution of systems of linear equations

IB Mathematics Analysis and Approaches SL 1.2—arithmetic Sequences and Series Notes

Arithmetic Sequences

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant.

This constant difference is called the common difference, typically denoted by $d$.

Definition and Notation

For an arithmetic sequence $u_1, u_2, u_3, ...$, where $u_n$ represents the $n$th term:

$$u_n = u_{n-1} + d$$

where $d$ is the common difference.

Example

Consider the sequence: 3, 7, 11, 15, 19, ...
Here, $a_1 = 3$ and the common difference $d = 4$.

Note

Terms can also be represented as $a_n$ instead of $u_n$.
The two notations are interchangeable.

Formula for the nth Term

The general formula for the $n$th term of an arithmetic sequence is: $$u_n = u_1 + (n-1)d$$ where

$u_1$ is the first term, $n$ is the position of the term
$d$ is the common difference

This is because for every term, you're adding $d$ to the previous term.

To get to the $n$th term from the first term, you perform $n - 1$ additions of $d$.

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IB Mathematics Analysis and Approaches SL 1.2—arithmetic Sequences and Series Notes

Arithmetic Sequences

Definition and Notation

Formula for the nth Term

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Arithmetic Sequences

Definition and Notation

Formula for the nth Term

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Number and Algebra16 subtopics

Functions16 subtopics

Geometry & Trigonometry18 subtopics

Statistics & Probability14 subtopics

Calculus19 subtopics

IB Mathematics Analysis and Approaches SL 1.2—arithmetic Sequences and Series Notes

Arithmetic Sequences

Definition and Notation

Formula for the nth Term

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Arithmetic Sequences

Definition and Notation

Formula for the nth Term

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Number and Algebra16 subtopics

Functions16 subtopics

Geometry & Trigonometry18 subtopics

Statistics & Probability14 subtopics

Calculus19 subtopics