[H2_20150512GSS] A Square Spiral in Geometric Progression

Question

Introduction

     This is a type of question that has become quite common in H2 Mathematics at Junior College level.  I was not told where this question came from, but I seem to get a bout of déjà vu.  It is quite a common practice for the Singapore junior colleges to mimic questions from the GCE ‘A’ Levels and/or one another.

Solution

Summary

     The keys to solving this question are:-

          (1)  if a coordinate frame is needed but not given it the question, we invent our own.

          (2)  see whether we need to care about the direction or not, and then apply the
                 geometric series formula.

          (3)  When applying the geometric series formula, always identify correctly the first term,
                 the common ratio, and the number of terms to be summed.

Heuristics Used

H02. Use a diagram / model

H04. Look for pattern(s)

H09. Restate the problem in another way

H10. Simplify the problem

H11. Solve part of the problem

H13* Use Equation / write a Mathematical Sentence

Suitable Levels

* GCE ‘A’ Level H2 Mathematics

* other syllabuses that involve geometric series