ACT Exam > ACT Questions > The third term of a G.P. is 9. The product of...
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The third term of a G.P. is 9. The product of its first five terms is
- a)35
- b)39
- c)310
- d)312
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The third term of a G.P. is 9. The product of its first five terms isa...
Concept:
Five terms in a geometric progression:
If a G.P. has first term a and common ratio r then the five consecutive terms in the GP are of the form a/r2, a/r, a, ar, ar2 .
Five terms in a geometric progression:
If a G.P. has first term a and common ratio r then the five consecutive terms in the GP are of the form a/r2, a/r, a, ar, ar2 .
Calculation:
Let us consider a general geometric progression with common ratio r.
Assume that the five terms in the GP are
It is given that third term is 9.
Therefore, a = 9.
Now the product of the five terms is given as follows:
Let us consider a general geometric progression with common ratio r.
Assume that the five terms in the GP are
It is given that third term is 9.
Therefore, a = 9.
Now the product of the five terms is given as follows:
But we know that a = 9.
Thus, the product is 95 = 310.
Thus, the product is 95 = 310.
Most Upvoted Answer
The third term of a G.P. is 9. The product of its first five terms isa...
Given Information:
- The third term of the geometric progression (G.P.) is 9.
- The product of the first five terms of the G.P. needs to be determined.
Formula for the nth term of a G.P.:
The nth term of a geometric progression is given by: \( a_n = a_1 \times r^{(n-1)} \)
Finding the first term:
Let the first term of the G.P. be 'a' and the common ratio be 'r'.
Given that the third term is 9, we can write: \( a_3 = a \times r^2 = 9 \)
Calculating the first term 'a':
From the above equation, we can find the value of 'a' by substituting the values: \( a \times r^2 = 9 \)
Since the third term is 9, we have: \( a = \frac{9}{r^2} \)
Product of the first five terms:
The product of the first five terms of the G.P. is: \( a_1 \times a_2 \times a_3 \times a_4 \times a_5 \)
Substituting the values:
We know that the third term is 9, and we can find the first term 'a' in terms of 'r'. By substituting these values into the product of the first five terms formula, we can calculate the product.
Calculating the product:
Substitute the value of 'a' in terms of 'r' into the product formula and simplify to find the product of the first five terms of the G.P.
Final Answer:
After simplifying the product, the correct answer is option 'c) 310'.
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The third term of a G.P. is 9. The product of its first five terms isa)35b)39c)310d)312Correct answer is option 'C'. Can you explain this answer?
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The third term of a G.P. is 9. The product of its first five terms isa)35b)39c)310d)312Correct answer is option 'C'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The third term of a G.P. is 9. The product of its first five terms isa)35b)39c)310d)312Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The third term of a G.P. is 9. The product of its first five terms isa)35b)39c)310d)312Correct answer is option 'C'. Can you explain this answer?.
The third term of a G.P. is 9. The product of its first five terms isa)35b)39c)310d)312Correct answer is option 'C'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The third term of a G.P. is 9. The product of its first five terms isa)35b)39c)310d)312Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The third term of a G.P. is 9. The product of its first five terms isa)35b)39c)310d)312Correct answer is option 'C'. Can you explain this answer?.
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