Geometric progression
Answers are for parents and teachers.
1
Find the common ratio and b₆ of 2, 10, 50, ...
q = 5, b₆ = 6250
2
If b₂ = 6 and b₅ = 162, find q and b₁.
q = 3, b₁ = 2
3
Is 640 a term of 5, 10, 20, ...? Find its index.
Yes: 5 · 2^(n−1) = 640, 2^(n−1) = 128 = 2⁷, so n = 8.
4
Prove that b_n = 3 · 4ⁿ is a geometric progression.
b_(n+1) : b_n = (3 · 4^(n+1)) : (3 · 4ⁿ) = 4, which does not depend on n.
5
Find the positive geometric mean of 4 and 25.
10