Arithmetic and geometric sequences
Arithmetic and geometric sequences for IB Analysis and Approaches HL: general term, sums, infinite sum, compound interest, growth and worked IB questions.
A sequence is a list of numbers that follows a fixed rule: always adding the same amount (arithmetic) or always multiplying by the same amount (geometric). With two formulas for the general term and two for the sum you can solve almost everything the IB asks about sequences, including the sum of infinitely many terms and problems on compound interest, growth and depreciation.
Recommended order
Study the arithmetic sequences first, then the geometric sequences (with the infinite sum), and finish with the applications, which combine the formulas with the logarithms from topic 2. At the end you have the IB exam questions grouped by type.
Powers and logarithms (topics 1 and 2) and systems of two equations.
Sections in this topic
Arithmetic sequences: general term, sum and sigma notation
Sequences, sigma notation and arithmetic sequences: general term, common difference, sum of n terms with proof and how many terms to add, in IB AA HL.
3 worked examples Section 2Geometric sequences and infinite sums
Common ratio, general term and sum of a geometric sequence, and the infinite sum with |r|<1 and recurring decimals, for IB Analysis and Approaches HL.
3 worked examples Section 3Simple and compound interest, growth and depreciation
Simple and compound interest compounded k times a year, growth, depreciation and time to reach a target, for IB Analysis and Approaches HL.
3 worked examples End of topicIB exam questions: topic 3
IB exam questions on arithmetic and geometric sequences, infinite sums and compound interest (Analysis and Approaches HL), with worked solutions.
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