Math Problem Statement
The first and third terms of a geometric sequence are shown in the table below. What is the second term?
Solution
To find the second term in a geometric sequence given the first term and the third term , follow these steps:
Step 1: Set up the formula for a geometric sequence
In a geometric sequence, each term is found by multiplying the previous term by a common ratio .
The general formula for the th term is:
Step 2: Apply the formula to the given terms
- For the first term ():
- For the third term ():
Step 3: Solve for the common ratio
Divide both sides by 3: Take the square root of both sides:
Step 4: Find the second term
Using the common ratio :
Answer: The second term is 15.
Would you like to explore more about geometric sequences, or do you have other questions?
Related Questions:
- How would the sequence change if the common ratio were negative?
- What is the formula for the sum of the first terms of a geometric sequence?
- How can you find the th term if you know the sum of the first terms?
- Can a geometric sequence have a common ratio of 1? What would it look like?
- What is the product of the first and third terms in this sequence?
- How do geometric sequences differ from arithmetic sequences?
- What happens to the terms of a geometric sequence as increases if the common ratio is between 0 and 1?
- What would be the fourth term in this sequence?
Tip: In geometric sequences, recognizing the relationship between the terms through the common ratio helps solve for unknown terms quickly.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Geometric Sequences
Formulas
Formula for the nth term of a geometric sequence
Theorems
-
Suitable Grade Level
Grades 9-12
Related Recommendation
Find the First Term of a Geometric Sequence with Given Terms
Calculate the First Term of a Geometric Sequence with Given Terms
Finding the First Term of a Geometric Sequence Given a2 = 6 and r = 3
Calculate the 7th Term of a Geometric Sequence with Given First Term and Third Term
Find the 5th Term of a Geometric Sequence (a1 = 3, r = 6)