Write the geometric sequence with positive terms whose second term is 9 and fourth term is 1.
Let's call the first term "a" and the common ratio "r". Then we know:
- Second term = a * r = 9
- Fourth term = a * r^3 = 1
We can use these two equations to solve for "a" and "r". Here's one way to do it:
- Divide the second equation by the first: (a * r^3) / (a * r) = 1 / 9
- Simplify: r^2 = 1/9
- Take the square root of both sides: r = 1/3
- Substitute this value of r into the second equation: a * (1/3)^3 = 1
- Simplify: a/27 = 1
- Multiply both sides by 27: a = 27
So the sequence is: 27, 9, 3, 1, ...
Each term is obtained by multiplying the previous term by 1/3.