Mastering Mathematics Smartly by Wee Wen Shih

A unique self-help website that provides comprehensive coverage of mathematics at A-level & beyond, written in a student-friendly style.

Arithmetic & geometric progressions

This 4-page document highlights the essentials for AP & GP.

Try these questions:
N97/Paper 1/Q15, N99/Paper 1/Q14(a), N01/Paper 1/Q14

Problem involving repayments

Many students find this type of problem difficult:

The solving approach is systematic in nature:

Finally, it is necessary to observe the pattern and conclude the use of AP or GP or their combination.

Application of other topics

A question on AP/GP may involve the application of knowledge from other topics, such as logarithms and exponential functions, where the examiner assumes that students have acquired these at O-level.

Consider the following question: Let x_1, x_2, x_3, ... be a sequence of numbers where \text{log}_a\:x_{n+1} - 1 = \text{log}_a\:x_n for n \ge 1. It is given that x_1 + x_2 + ... + x_{100} = 100. Find x_{101} + x_{102} + ... + x_{200} in terms of a.

Rest of the content coming soon...