Practice30Create account

Class 10 Geometric Patterns — practice questions with answers

Algebra — Sequences · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Find the next term in the pattern: 2, 6, 18, 54, ...
Show answer
Answer: B) 162
Each term is multiplied by 3 (common ratio = 3). So next term = 54 x 3 = 162.
2. Which term of the pattern 2, 6, 18, 54, ... has the value 486?
Show answer
Answer: B) 6th
a r^(n-1) = 2 x 3^(n-1) = 486 gives 3^(n-1) = 243 = 3⁵, so n - 1 = 5, n = 6.
3. What is the 7th term of the pattern 1, 2, 4, 8, ...?
Show answer
Answer: B) 64
7th term = 2^(7-1) = 2⁶ = 64.
4. A geometric pattern has 3rd term 20 and 5th term 80.
Given all terms are positive, find the common ratio.
Show answer
Answer: A) 2
5th/3rd = r² = = 4, so r = 2 (positive terms).
5. A geometric pattern of triangle perimeters is 48, 24, 12, ... cm, where each triangle's perimeter is half the previous one.
The pattern continues forever. What is the sum of all the perimeters (48 + 24 + 12 + ...)?
Show answer
Answer: A) 96 cm
Infinite sum of a geometric pattern with first term 48 and ratio = = 96 cm.
Practise all 50 questions free →

10 free questions a day without an account — unlimited with a free account.