This article covers the essential skills of geometric sequences – a core topic in DSE Paper 1 Section A(1) and A(2) worth 4–6 marks. You will learn the definition of a geometric sequence, the general term formula
, the sum of first n terms formula, and how to solve application problems involving geometric means, compound interest, population growth, and more. The article includes step-by-step worked examples, DSE exam techniques, practice questions. These are essential skills that appear regularly in DSE papers.
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Geometric Sequences | General Term & Sum of First n Terms
Question 1 MC
Find the 5th term of the geometric sequence \( 5, 10, 20, 40, \ldots \).
A. \( 80 \) B. \( 160 \) C. \( 320 \) D. \( 640 \)
Question 2 MC
What is the sum of the first 5 terms of \( 2, -4, 8, -16, \ldots \)?
A. \( 22 \) B. \( -22 \) C. \( 10 \) D. \( -10 \)
Question 3 Short Answer
Find the general term of the geometric sequence \( 81, 27, 9, 3, \ldots \).
Question 4 Short Answer
How many terms are in the geometric sequence \( 4, 12, 36, \ldots, 8748 \)?
Question 5 MC
If \( x, 2x+1, 4x+3 \) are consecutive terms of a geometric sequence, find \( x \).
A. \( 1 \) B. \( -1 \) C. \( 2 \) D. \( -2 \)
Question 6 Short Answer
Insert 3 geometric means between 2 and 162.
Question 7 MC
The 3rd term of a geometric sequence is 18 and the 6th term is 486. Find the common ratio.
A. \( 3 \) B. \( 2 \) C. \( 4 \) D. \( 5 \)
Question 8 Short Answer
A population of 1000 bacteria triples every hour. How many bacteria will there be after 4 hours?
Question 9 Short Answer
Find the sum of the first 7 terms of the geometric sequence \( 4, 12, 36, \ldots \).
Question 10 Short Answer
A car depreciates at 15% per year. If its initial value is $200,000, find its value after 5 years.
When using the sum formula \( S_n = \frac{a(1-r^n)}{1-r} \), remember that it only works for \( r \neq 1 \). If \( r = 1 \), simply use \( S_n = na \).