Geometric Progressions – nth Term, Sum, Infinite GP

Grade 11 Maths Higher — Geometric Progressions – nth Term, Sum, Infinite GP: 25 practice questions with instant scoring and explanations.

1. A geometric progression (GP) is a sequence where:
2. The nth term of a GP with first term a and common ratio r is:
3. For the GP 2, 6, 18, 54, ..., the common ratio is:
4. The sum of first n terms of a GP with a ≠ 0 and r ≠ 1 is:
5. The sum of an infinite GP with |r| < 1 is:
6. For an infinite GP to have a finite sum, the condition is:
7. The 5th term of the GP 1, 2, 4, 8, ... is:
8. The sum of first 6 terms of the GP 2, 4, 8, ... is:
9. The sum of the infinite GP 1 + 1/2 + 1/4 + 1/8 + ... is:
10. If the first term of a GP is 3 and the 4th term is 81, the common ratio is:
11. If a, ar, ar² are three consecutive terms, then the third term in terms of first two is:
12. The sum 1 + 2 + 4 + ... + 512 is:
13. In a GP, if a = 1 and r = 2, then the sum of the first 10 terms is:
14. The sum 1 - 1/2 + 1/4 - 1/8 + ... is:
15. For the infinite GP 0.3 + 0.03 + 0.003 + ..., the sum is:
16. The geometric mean of two numbers a and b is:
17. If p, q, r are in GP, then:
18. The sum of the GP 1/2 + 1/4 + 1/8 + ... + 1/128 is:
19. If the first term is a and the sum to infinity is 4a, then the common ratio is:
20. In a GP, if the 3rd term is 4 and the 6th term is 32, the first term is:
21. The repeating decimal 0.777... equals:
22. For which value of r does the sum of infinite GP become undefined?
23. The sum of the GP 8, 4, 2, 1, ... to infinity is:
24. If a GP has 5 terms with first term 2 and last term 162, the sum is:
25. The sum 2 + 6 + 18 + ... + 2·3⁶ equals: