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in a sequence of 21 terms the first 11 terms are u in ap with common difference 2 and the last 11 terms are in gp with common ratio 2 if the middle term of the ap is equal to the right middle term of gp the middle term of the entire sequences is
Most Upvoted Answer
in a sequence of 21 terms the first 11 terms are u in ap with common d...
The middle term of the AP is the 6th term, therefore,
6th term= a+(6-1)d= a+10
The middle term of the GP is the 6th term,
6th term = A(2)^5= 32A
Hence= 32A = a+10 (1)
The first term of GP=11th term of AP, therefore
A= a+10*2=a+20 (2)
From 1 and 2,
a= -630/31
From (2), A= a+20 therefore A= -10/31
As the middle term of the sequence is the first term of the GP,
Hence answer is -10/31
Community Answer
in a sequence of 21 terms the first 11 terms are u in ap with common d...
Explanation:
Understanding the Given Conditions:
- We are given a sequence of 21 terms, with the first 11 terms forming an arithmetic progression (AP) with a common difference of 2.
- The last 11 terms form a geometric progression (GP) with a common ratio of 2.
- The middle term of the AP is equal to the right middle term of the GP.
Finding the Middle Term of the AP:
- Since the first term of the AP is u, the middle term can be calculated using the formula for the middle term of an AP:
Middle term of AP = u + (n/2 - 1) * d, where n is the total number of terms and d is the common difference.
- In this case, n = 11 and d = 2, so the middle term of the AP is u + 10 * 2 = u + 20.
Finding the Right Middle Term of the GP:
- The right middle term of a GP can be calculated using the formula:
Right middle term of GP = a * r^(n/2 - 1), where a is the first term of the GP, r is the common ratio, and n is the total number of terms.
- In this case, a is the 11th term of the sequence, which can be calculated as u + 10 * 2 = u + 20.
- Therefore, the right middle term of the GP is (u + 20) * 2^(11/2 - 1) = (u + 20) * 2^5 = (u + 20) * 32 = 32u + 640.
Finding the Middle Term of the Entire Sequence:
- Since the middle term of the AP is u + 20 and the right middle term of the GP is 32u + 640, we can set them equal to each other:
u + 20 = 32u + 640
Solving this equation will give us the value of u, which can then be used to find the middle term of the entire sequence.
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in a sequence of 21 terms the first 11 terms are u in ap with common difference 2 and the last 11 terms are in gp with common ratio 2 if the middle term of the ap is equal to the right middle term of gp the middle term of the entire sequences is
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in a sequence of 21 terms the first 11 terms are u in ap with common difference 2 and the last 11 terms are in gp with common ratio 2 if the middle term of the ap is equal to the right middle term of gp the middle term of the entire sequences is for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about in a sequence of 21 terms the first 11 terms are u in ap with common difference 2 and the last 11 terms are in gp with common ratio 2 if the middle term of the ap is equal to the right middle term of gp the middle term of the entire sequences is covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for in a sequence of 21 terms the first 11 terms are u in ap with common difference 2 and the last 11 terms are in gp with common ratio 2 if the middle term of the ap is equal to the right middle term of gp the middle term of the entire sequences is.
in a sequence of 21 terms the first 11 terms are u in ap with common difference 2 and the last 11 terms are in gp with common ratio 2 if the middle term of the ap is equal to the right middle term of gp the middle term of the entire sequences is for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about in a sequence of 21 terms the first 11 terms are u in ap with common difference 2 and the last 11 terms are in gp with common ratio 2 if the middle term of the ap is equal to the right middle term of gp the middle term of the entire sequences is covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for in a sequence of 21 terms the first 11 terms are u in ap with common difference 2 and the last 11 terms are in gp with common ratio 2 if the middle term of the ap is equal to the right middle term of gp the middle term of the entire sequences is.
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