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The sum of 4th term and 8th term of an AP is 24 and the sum of the 6th and 10th term is 44. Find the first three terms Of AP?
Most Upvoted Answer
The sum of 4th term and 8th term of an AP is 24 and the sum of the 6th...
Solution:
Given:
- Sum of 4th and 8th term of an AP is 24
- Sum of 6th and 10th term is 44
To Find:
- First three terms of AP
Explanation:
Let us assume the first term of the AP is 'a' and the common difference is 'd'. Then the fourth term will be 'a+3d', the sixth term will be 'a+5d', the eighth term will be 'a+7d', and the tenth term will be 'a+9d'.
Equation 1:
- Sum of 4th and 8th term of an AP is 24
(a+3d) + (a+7d) = 24
2a + 10d = 24
a + 5d = 12
Equation 2:
- Sum of 6th and 10th term of an AP is 44
(a+5d) + (a+9d) = 44
2a + 14d = 44
a + 7d = 22
Solving the Equations:
- Subtract Equation 1 from Equation 2
(a+7d) - (a+5d) = 22 - 12
2d = 10
d = 5
- Substitute the value of 'd' in Equation 1 or 2
a + 5(5) = 12 OR a + 7(5) = 22
a = -13 OR a = -3
Answer:
Therefore, the first three terms of the AP can be:
- -13, -8, -3 (when a = -13)
- -3, 2, 7 (when a = -3)
Conclusion:
The first three terms of the AP can be -13, -8, -3 or -3, 2, 7 depending on the value of 'a'.
Community Answer
The sum of 4th term and 8th term of an AP is 24 and the sum of the 6th...
a4+a8=24a6+a10=44thena+3d+a+7d=242a+10d=24. equation no. 1a+5d+a+9d=442a+14d=44. equation no. 2From equation no. 1 & equation no. 2so. a= -13and d= 5 first term (a) =-13second term (a+d)= -8third term (a+2d) = -3
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The sum of 4th term and 8th term of an AP is 24 and the sum of the 6th and 10th term is 44. Find the first three terms Of AP?
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The sum of 4th term and 8th term of an AP is 24 and the sum of the 6th and 10th term is 44. Find the first three terms Of AP? 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 The sum of 4th term and 8th term of an AP is 24 and the sum of the 6th and 10th term is 44. Find the first three terms Of AP? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of 4th term and 8th term of an AP is 24 and the sum of the 6th and 10th term is 44. Find the first three terms Of AP? .
The sum of 4th term and 8th term of an AP is 24 and the sum of the 6th and 10th term is 44. Find the first three terms Of AP? 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 The sum of 4th term and 8th term of an AP is 24 and the sum of the 6th and 10th term is 44. Find the first three terms Of AP? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of 4th term and 8th term of an AP is 24 and the sum of the 6th and 10th term is 44. Find the first three terms Of AP? .
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