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Questions and Answers
What is the formula for the nth term of a geometric sequence?
What is the formula for the nth term of a geometric sequence?
- $$T_n = a \cdot r^n$$
- $$T_n = a \cdot r^{n-1}$$ (correct)
- $$T_n = a \cdot r^{n+1}$$
- $$T_n = a \cdot r^{n-2}$$
What is the purpose of multiplying both sides of the equation by r when deriving the formula for a finite geometric series?
What is the purpose of multiplying both sides of the equation by r when deriving the formula for a finite geometric series?
- To find the common ratio
- To create a new equation to subtract from the original (correct)
- To simplify the equation
- To eliminate the first term
What is the condition for using the alternative formula for a finite geometric series?
What is the condition for using the alternative formula for a finite geometric series?
- r < 1
- r = 1
- r > 1 (correct)
- r 1
What is the result of subtracting the second equation from the first when deriving the formula for a finite geometric series?
What is the result of subtracting the second equation from the first when deriving the formula for a finite geometric series?
What is the general formula for the sum of a finite geometric series?
What is the general formula for the sum of a finite geometric series?
What is the term used to describe the constant value by which each term in a geometric sequence is multiplied to obtain the next term?
What is the term used to describe the constant value by which each term in a geometric sequence is multiplied to obtain the next term?
What is the value of the common ratio 'r' in a geometric sequence if the second term is 6 and the first term is 3?
What is the value of the common ratio 'r' in a geometric sequence if the second term is 6 and the first term is 3?
What is the sum of the first 5 terms of a geometric sequence if the first term is 2 and the common ratio is 3?
What is the sum of the first 5 terms of a geometric sequence if the first term is 2 and the common ratio is 3?
Which of the following is NOT a condition for using the alternative formula for a finite geometric series?
Which of the following is NOT a condition for using the alternative formula for a finite geometric series?
What is the value of 'a' in a geometric sequence if the sum of the first 4 terms is 15 and the common ratio is 2?
What is the value of 'a' in a geometric sequence if the sum of the first 4 terms is 15 and the common ratio is 2?
What is the formula for the sum of a finite geometric series when the common ratio 'r' is less than 1?
What is the formula for the sum of a finite geometric series when the common ratio 'r' is less than 1?
What is the value of the sum of the first 3 terms of a geometric sequence if the first term is 2 and the common ratio is -2?
What is the value of the sum of the first 3 terms of a geometric sequence if the first term is 2 and the common ratio is -2?
If the sum of the first n terms of a geometric sequence is 15 and the common ratio is 2, what can be said about the value of the first term?
If the sum of the first n terms of a geometric sequence is 15 and the common ratio is 2, what can be said about the value of the first term?
What happens to the value of S_n as n approaches infinity if |r| > 1?
What happens to the value of S_n as n approaches infinity if |r| > 1?
If the sum of the first 5 terms of a geometric sequence is 242 and the common ratio is 3, what is the value of the first term?
If the sum of the first 5 terms of a geometric sequence is 242 and the common ratio is 3, what is the value of the first term?
What is the relationship between the sum of the first n terms of a geometric sequence and the sum of the first (n - 1) terms?
What is the relationship between the sum of the first n terms of a geometric sequence and the sum of the first (n - 1) terms?
If the sum of the first n terms of a geometric sequence is 15 and the sum of the first (n - 1) terms is 7.5, what is the value of the common ratio?
If the sum of the first n terms of a geometric sequence is 15 and the sum of the first (n - 1) terms is 7.5, what is the value of the common ratio?
What is the sum of the first n terms of a geometric sequence if the common ratio is -1 and the first term is 1?
What is the sum of the first n terms of a geometric sequence if the common ratio is -1 and the first term is 1?
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