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two ap's have the same common difference . the first two terms of one of these is -3 and not the other is -7 .Find the difference between their 4th terms.
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2APs have the same common difference the 1ofthat is -5 and the other is -8 find the difference between them?
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two ap's have the same common difference . the first two terms of one ...
Understanding Arithmetic Progressions (AP)
An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant. This constant is known as the common difference (d).
Given Information
- Two APs with the same common difference (d).
- First AP: First term (a1) = -3
- Second AP: First term (a2) = -7
Finding the Terms
For an AP, the nth term can be expressed as:
- For the first AP:
- Tn1 = a1 + (n-1)d
- For the second AP:
- Tn2 = a2 + (n-1)d
Calculating the 4th Terms
1. 4th term of the first AP:
- T4_1 = -3 + (4-1)d
- T4_1 = -3 + 3d
2. 4th term of the second AP:
- T4_2 = -7 + (4-1)d
- T4_2 = -7 + 3d
Finding the Difference
To find the difference between the 4th terms of both APs, we calculate:
- Difference = T4_1 - T4_2
- Difference = (-3 + 3d) - (-7 + 3d)
Simplifying the Expression
- The common difference (3d) cancels out:
- Difference = -3 + 3d + 7 - 3d
- Difference = 4
Conclusion
The difference between the 4th terms of the two arithmetic progressions is 4. This demonstrates that while the starting points of the sequences differ, their progression remains consistent due to the common difference.
An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant. This constant is known as the common difference (d).
Given Information
- Two APs with the same common difference (d).
- First AP: First term (a1) = -3
- Second AP: First term (a2) = -7
Finding the Terms
For an AP, the nth term can be expressed as:
- For the first AP:
- Tn1 = a1 + (n-1)d
- For the second AP:
- Tn2 = a2 + (n-1)d
Calculating the 4th Terms
1. 4th term of the first AP:
- T4_1 = -3 + (4-1)d
- T4_1 = -3 + 3d
2. 4th term of the second AP:
- T4_2 = -7 + (4-1)d
- T4_2 = -7 + 3d
Finding the Difference
To find the difference between the 4th terms of both APs, we calculate:
- Difference = T4_1 - T4_2
- Difference = (-3 + 3d) - (-7 + 3d)
Simplifying the Expression
- The common difference (3d) cancels out:
- Difference = -3 + 3d + 7 - 3d
- Difference = 4
Conclusion
The difference between the 4th terms of the two arithmetic progressions is 4. This demonstrates that while the starting points of the sequences differ, their progression remains consistent due to the common difference.
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two ap's have the same common difference . the first two terms of one of these is -3 and not the other is -7 .Find the difference between their 4th terms.
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two ap's have the same common difference . the first two terms of one of these is -3 and not the other is -7 .Find the difference between their 4th 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 ap's have the same common difference . the first two terms of one of these is -3 and not the other is -7 .Find the difference between their 4th terms. covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for two ap's have the same common difference . the first two terms of one of these is -3 and not the other is -7 .Find the difference between their 4th terms..
two ap's have the same common difference . the first two terms of one of these is -3 and not the other is -7 .Find the difference between their 4th 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 ap's have the same common difference . the first two terms of one of these is -3 and not the other is -7 .Find the difference between their 4th terms. covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for two ap's have the same common difference . the first two terms of one of these is -3 and not the other is -7 .Find the difference between their 4th terms..
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