- #1
EricPowell
- 26
- 0
Homework Statement
Write the first 5 terms of the geometric sequence
3, __ , 32x+1, __, __
Homework Equations
tn=arn-1
The Attempt at a Solution
tn=arn-1
32x+1=3r3-1
r2=32x+1 / 3
r=√32x+1 / √3
I'm stuck
Villyer said:Before taking the square root, try to simplyfy the right side. What is [itex]\frac{3^{2x+1}}{3^{1}}[/itex]?
A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant number called the common ratio. For example, in the sequence 2, 4, 8, 16, the common ratio is 2.
To find the missing terms in a geometric sequence, you can use the formula an = a1 * r^(n-1), where an is the nth term, a1 is the first term, and r is the common ratio. Plug in the known values and solve for the missing term.
Yes, there can be more than one missing term in a geometric sequence. As long as the common ratio remains the same, the sequence will still be considered geometric.
You can check if your answer for the missing terms is correct by plugging them back into the original sequence and seeing if it follows the pattern of multiplying by the common ratio. You can also use a calculator to check your work.
Yes, geometric sequences can be found in many real-life scenarios, such as population growth, compound interest, and bacterial growth. They can also be used in geometric constructions, such as creating spirals and fractals.