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The third term of a GP is 3. What is the product of the first five terms?
Correct answer is '243'. Can you explain this answer?
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The third term of a GP is 3. What is the product of the first five te...
Given:
- The third term of a GP is 3.
To find:
- The product of the first five terms.
Approach:
- Let's assume the first term of the GP is 'a' and the common ratio is 'r'.
- We are given that the third term is 3, so we can write the equation as:
ar^2 = 3 ----(1)
Solving for a:
- We can express the first term 'a' in terms of the common ratio 'r' using equation (1).
- Dividing both sides of equation (1) by r^2, we get:
a = 3/r^2 ----(2)
Product of the first five terms:
- The product of the first five terms can be calculated by multiplying all the terms together.
- The first five terms of the GP can be expressed as: a, ar, ar^2, ar^3, ar^4.
Substituting the value of a from equation (2):
- The product of the first five terms can be written as:
P = (3/r^2) * (3/r) * 3 * 3r * 3r^2
= 3 * 3 * 3 * r * r^2 * r * 3/r * 3/r^2
= 3^5 * r^(1+2+3-2-2)
= 243 * r^0
= 243
Conclusion:
- The product of the first five terms of the geometric progression is 243.
- The third term of a GP is 3.
To find:
- The product of the first five terms.
Approach:
- Let's assume the first term of the GP is 'a' and the common ratio is 'r'.
- We are given that the third term is 3, so we can write the equation as:
ar^2 = 3 ----(1)
Solving for a:
- We can express the first term 'a' in terms of the common ratio 'r' using equation (1).
- Dividing both sides of equation (1) by r^2, we get:
a = 3/r^2 ----(2)
Product of the first five terms:
- The product of the first five terms can be calculated by multiplying all the terms together.
- The first five terms of the GP can be expressed as: a, ar, ar^2, ar^3, ar^4.
Substituting the value of a from equation (2):
- The product of the first five terms can be written as:
P = (3/r^2) * (3/r) * 3 * 3r * 3r^2
= 3 * 3 * 3 * r * r^2 * r * 3/r * 3/r^2
= 3^5 * r^(1+2+3-2-2)
= 243 * r^0
= 243
Conclusion:
- The product of the first five terms of the geometric progression is 243.
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Community Answer
The third term of a GP is 3. What is the product of the first five te...
Given: The third term of a GP is 3.
Let 'a' be the first term and 'r' be the common ratio.
∴ T3 = ar2 = 3
We know that Tn = arn−1
So, T1 = a, T2 = ar, T3 = ar2, T4 = ar3, T5 = ar4
Now, Product of the first five terms = a × ar × ar2 × ar3 × ar4 = a5r10 = (ar2)5 = 35 = 243
Hence, the correct answer is 243.
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The third term of a GP is 3. What is the product of the first five terms?Correct answer is '243'. Can you explain this answer?
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The third term of a GP is 3. What is the product of the first five terms?Correct answer is '243'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The third term of a GP is 3. What is the product of the first five terms?Correct answer is '243'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The third term of a GP is 3. What is the product of the first five terms?Correct answer is '243'. Can you explain this answer?.
The third term of a GP is 3. What is the product of the first five terms?Correct answer is '243'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The third term of a GP is 3. What is the product of the first five terms?Correct answer is '243'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The third term of a GP is 3. What is the product of the first five terms?Correct answer is '243'. Can you explain this answer?.
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