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If 8th term of an Ap is the GM of the 1st & 22nd term of the same A. P. Find the common difference of the AP given that the sum of the first 22 terms is 770?
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If 8th term of an Ap is the GM of the 1st & 22nd term of the same A. P...
Given information:
- 8th term of the AP is the geometric mean of the 1st and 22nd terms of the same AP.
- Sum of the first 22 terms is 770.
Finding the common difference:
Let the common difference of the AP be d.
The 8th term = a + 7d
The 1st term = a
The 22nd term = a + 21d
According to the given information,
a + 7d = √(a * (a + 21d))
Squaring both sides,
(a + 7d)^2 = a * (a + 21d)
Expanding and simplifying,
a^2 + 14ad + 49d^2 = a^2 + 21ad
Rearranging terms,
7ad - 28d^2 = 0
7d(a - 4d) = 0
Since d ≠ 0, we have a - 4d = 0
Therefore, a = 4d
Sum of the first 22 terms:
The sum of the first n terms of an AP is given by Sn = n/2 * (2a + (n-1)d)
Given that the sum of the first 22 terms is 770,
22/2 * (2(4d) + (22-1)d) = 770
11 * (8d + 21d) = 770
11 * 29d = 770
319d = 770
d = 770/319
d ≈ 2.41
Therefore, the common difference of the AP is approximately 2.41.
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If 8th term of an Ap is the GM of the 1st & 22nd term of the same A. P. Find the common difference of the AP given that the sum of the first 22 terms is 770?
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If 8th term of an Ap is the GM of the 1st & 22nd term of the same A. P. Find the common difference of the AP given that the sum of the first 22 terms is 770? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If 8th term of an Ap is the GM of the 1st & 22nd term of the same A. P. Find the common difference of the AP given that the sum of the first 22 terms is 770? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 8th term of an Ap is the GM of the 1st & 22nd term of the same A. P. Find the common difference of the AP given that the sum of the first 22 terms is 770?.
If 8th term of an Ap is the GM of the 1st & 22nd term of the same A. P. Find the common difference of the AP given that the sum of the first 22 terms is 770? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If 8th term of an Ap is the GM of the 1st & 22nd term of the same A. P. Find the common difference of the AP given that the sum of the first 22 terms is 770? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 8th term of an Ap is the GM of the 1st & 22nd term of the same A. P. Find the common difference of the AP given that the sum of the first 22 terms is 770?.
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