Math Problem Statement
Solution
Let's solve the problem step by step based on the given formula for the sequence:
The formula for the -th term of the sequence is:
(a) Find the first five terms:
We calculate and by substituting into the formula.
Thus, the first five terms are:
(b) Find the common ratio :
The common ratio in a geometric sequence is the ratio between consecutive terms:
Using and :
Thus, the common ratio is:
Final Answer:
(a) First five terms:
(b) Common ratio:
Let me know if you'd like a detailed explanation of any part! 😊
Here are five related questions to deepen your understanding:
- What is the general formula for the sum of the first terms of a geometric sequence?
- How does the sign of affect the terms of the sequence?
- If , what happens to the sequence as ?
- What would and be for this sequence?
- How would the sequence change if instead of ?
Tip: Always confirm the common ratio by calculating the ratio for multiple consecutive terms to ensure consistency in a geometric sequence.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Sequences
Geometric Sequence
Formulas
nth term of a geometric sequence: a_n = a * r^(n-1)
Common ratio: r = a_(n+1) / a_n
Theorems
Properties of geometric sequences
Suitable Grade Level
Grades 9-11
Related Recommendation
8th Term of a Geometric Sequence with First Term 5 and Common Ratio 13
Geometric Sequence with First Term 5 and Common Ratio 6 - Find the 5th Term
Find the First Six Terms of a Geometric Sequence with a1 = 1/2 and r = 1/2
Find the Negative Common Ratio in a Geometric Progression with Given First and Fifth Terms
Find the 8th Term of a Geometric Sequence with First Term 100