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Asked by Nikhil Last Modified
Answer As an experienced tutor registered on UrbanPro, I'd be glad to help with this problem. UrbanPro is indeed an excellent platform for online coaching and tuition, providing students with access to quality education from skilled tutors.
Let's prove the given relation:
Given that the 5th, 8th, and 11th terms of a Geometric Progression (GP) are pp, qq, and ss respectively.
We know the formula for the nth term of a GP is an=ar(n−1)an=ar(n−1), where aa is the first term, and rr is the common ratio.
So, for the 5th term, a5=ar4=pa5=ar4=p
For the 8th term, a8=ar7=qa8=ar7=q
For the 11th term, a11=ar10=sa11=ar10=s
Now, let's form two equations using the given information:
From the 5th and 8th terms: q=ar7q=ar7
From the 8th and 11th terms: s=ar10s=ar10
Now, let's divide equation 2 by equation 1:
sq=ar10ar7=r10−7=r3qs=ar7ar10=r10−7=r3
So, we get q2=psq2=ps, which is the relation we wanted to prove.
Thus, it's verified that q2=psq2=ps holds true based on the given information. This proof reinforces the properties of geometric progressions and underscores the importance of understanding their terms and ratios. If you have any further questions or need clarification, feel free to ask! And remember, UrbanPro is here to support your academic journey every step of the way.
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