Geometric progressions: Class 11 practice
In a GP each term is r times the previous: aₙ = arⁿ⁻¹. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Exponents
- Fractions
The idea behind geometric progressions
In a GP each term is r times the previous: aₙ = arⁿ⁻¹. Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1, and the infinite sum is a/(1 − r) when |r| < 1.
Step-by-step method
- Find a and r.
- Use aₙ or Sₙ as needed.
- For an infinite sum, check |r| < 1 first.
Worked example 1 (Basic)
Find the 6th term of 5, 15, 45, …
- a = 5, r = 3
- a6 = 5 × (3)^5 = 1215
- Answer: 1215
Worked example 2 (Standard)
Find the sum of the first 4 terms of 4, -8, 16, …
- Sₙ = 4((-2)^4 − 1)/(-2 − 1)
- = -20
- Answer: -20
Worked example 3 (Challenge)
Find the sum to infinity of 6 + 6/2 + 6/4 + …
- r = 1/2
- S∞ = 6/(1 − 1/2) = 12
- Answer: 12
Common mistakes and misconceptions
- Using the AP formula
- Summing to infinity when |r| ≥ 1
Practice questions
- (Basic) Find the 4th term of 2, 4, 8, …
- (Basic) Find the 5th term of 6, -12, 24, …
- (Standard) Find the sum of the first 7 terms of 3, -6, 12, …
- (Standard) Find the sum of the first 6 terms of 4, 8, 16, …
- (Challenge) Find the sum to infinity of 2 + 2/2 + 2/4 + …
- (Challenge) Find the sum to infinity of 5 + 5/3 + 5/9 + …
Answer key with full working
- Q1: a = 2, r = 2 → a4 = 2 × (2)^3 = 16 → Answer: 16
- Q2: a = 6, r = -2 → a5 = 6 × (-2)^4 = 96 → Answer: 96
- Q3: Sₙ = 3((-2)^7 − 1)/(-2 − 1) → = 129 → Answer: 129
- Q4: Sₙ = 4((2)^6 − 1)/(2 − 1) → = 252 → Answer: 252
- Q5: r = 1/2 → S∞ = 2/(1 − 1/2) = 4 → Answer: 4
- Q6: r = 1/3 → S∞ = 5/(1 − 1/3) = 15/2 → Answer: 15/2
Syllabus note
This skill is listed under "Sequences and Series" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is geometric progressions in?
"Sequences and Series", Class 11 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.