Arithmetic and geometric sequences
Arithmetic and geometric sequences for IB Applications and Interpretation SL: general term, sums, interest, depreciation, loans and worked IB exercises.
This topic covers arithmetic and geometric sequences: how to find any term, how to add the first terms and, above all, how to apply them to money and growth: simple and compound interest, depreciation, population growth, annuities and loan amortization. In the Applications and Interpretation exam, almost all the problems in this topic are set in a real situation and solved with the graphic display calculator (GDC), so you need to know what data you are given and how to interpret its result.
Recommended order
Sections 1 to 3 are the foundation (general term and sums). Sections 4 and 5 are the applications to money, which come up most often in the exam. At the end of the topic you have the IB exam questions grouped by type.
Basic algebra, powers and percentages from ESO, and topic 1 of this course.
Sections in this topic
Sequences, progressions and the nth term
What a sequence is, how to recognise an arithmetic or geometric progression and find its nth term. IB Applications and Interpretation SL.
3 worked examples Section 2Sum of the first n terms of an arithmetic progression
Sum of the first n terms of an arithmetic progression: two formulas, contextual problems and the GDC. IB Applications and Interpretation SL.
3 worked examples Section 3Sum of a geometric progression
Sum of the first n terms of a geometric progression: formula, the case r=1, and finding n with logarithms or GDC. IB Applications and Interpretation SL.
3 worked examples Section 4Simple and compound interest, depreciation and growth
Simple and compound interest, compounding periods, annual depreciation and population growth, with examples. IB Applications and Interpretation SL.
3 worked examples Section 5Annuities and amortization
Annuities and loan amortization: future value, fixed instalments, amortization tables and the GDC (N, I%, PV, PMT, FV, P/Y, C/Y). IB Applications SL.
3 worked examples End of topicIB exam questions for topic 2
IB exam questions on sequences, simple and compound interest, depreciation, annuities and loan amortisation, by type and level, with step-by-step solutions.
107 exercises · 24 ★★★ levelStuck on this topic?
Tell us where you get lost and we will tell you how to tackle it. Álvaro replies on WhatsApp.
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