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Two A.Ps. have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
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Two A.Ps. have the same common difference. The difference between thei...
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Two A.Ps. have the same common difference. The difference between thei...
Understanding the Problem
In this scenario, we have two Arithmetic Progressions (A.P.s) with the same common difference. Let's denote the first A.P. as:
- First A.P.: a, a + d, a + 2d, ...
And the second A.P. as:
- Second A.P.: b, b + d, b + 2d, ...
Where:
- 'a' and 'b' are the first terms of the first and second A.P. respectively.
- 'd' is the common difference.
Finding the 100th Terms
The formula for the nth term of an A.P. is given by:
- nth term = first term + (n - 1) * common difference
Thus, the 100th terms can be expressed as follows:
- 100th term of the first A.P.: a + 99d
- 100th term of the second A.P.: b + 99d
According to the problem, the difference between their 100th terms is 100:
- (a + 99d) - (b + 99d) = 100
This simplifies to:
- a - b = 100
Finding the 1000th Terms
Now, let's find the 1000th terms of both A.P.s:
- 1000th term of the first A.P.: a + 999d
- 1000th term of the second A.P.: b + 999d
The difference between their 1000th terms is:
- (a + 999d) - (b + 999d)
This simplifies to:
- a - b = (a - b) + 0 = 100
Conclusion
The difference between the 1000th terms of both A.P.s is also 100.
Thus, the answer is:
- The difference between their 1000th terms is 100.
In this scenario, we have two Arithmetic Progressions (A.P.s) with the same common difference. Let's denote the first A.P. as:
- First A.P.: a, a + d, a + 2d, ...
And the second A.P. as:
- Second A.P.: b, b + d, b + 2d, ...
Where:
- 'a' and 'b' are the first terms of the first and second A.P. respectively.
- 'd' is the common difference.
Finding the 100th Terms
The formula for the nth term of an A.P. is given by:
- nth term = first term + (n - 1) * common difference
Thus, the 100th terms can be expressed as follows:
- 100th term of the first A.P.: a + 99d
- 100th term of the second A.P.: b + 99d
According to the problem, the difference between their 100th terms is 100:
- (a + 99d) - (b + 99d) = 100
This simplifies to:
- a - b = 100
Finding the 1000th Terms
Now, let's find the 1000th terms of both A.P.s:
- 1000th term of the first A.P.: a + 999d
- 1000th term of the second A.P.: b + 999d
The difference between their 1000th terms is:
- (a + 999d) - (b + 999d)
This simplifies to:
- a - b = (a - b) + 0 = 100
Conclusion
The difference between the 1000th terms of both A.P.s is also 100.
Thus, the answer is:
- The difference between their 1000th terms is 100.
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Two A.Ps. have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
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Two A.Ps. have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two A.Ps. have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two A.Ps. have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?.
Two A.Ps. have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two A.Ps. have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two A.Ps. have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?.
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