Mathematics
Mathematics
Problem
In a geometric progression, the 3rd term is 4 and the 5th term is 16. Which of the following gives the possible value(s) of the common ratio? a) b) c) d)Intuitive explanation
A geometric progression grows (or shrinks) by multiplying by the same factor each time—that's the common ratio . The key insight is that you can write any term using the first term and , then use your two known terms to set up equations and solve for . Since squaring is involved, you'll likely get two solutions, both of which are valid because a geometric sequence can have a negative common ratio and still produce positive terms.
Intuitive explanation
A geometric progression grows (or shrinks) by multiplying by the same factor each time—that's the common ratio . The key insight is that you can write any term using the first term and , then use your two known terms to set up equations and solve for . Since squaring is involved, you'll likely get two solutions, both of which are valid because a geometric sequence can have a negative common ratio and still produce positive terms.