Find the ratio of their $18^{\text {th }}$ terms. If the sum of first $p$ terms of an A.P. is equal to the sum of the first $q$ terms, then find the sum of the first $(p+q)$ terms.

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Precalculus

NCERT Class 11 - Math

Chapter 9

Sequences and Series

Section 2

Sequences

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Problem 1

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Problem 10

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Video Transcript

Hello. We have problem number 10. And this it is given that if the sum of our speed terms of an A. P. Is equal to some of us killed him. Some of first p terms of an ap equal to some of the first kingdoms rescue. Okay then find that some of us people school terms. So we have to find People secure. Some of us people secure it will be equal to and by two To a bless and -1. And today that we need to find out. Okay so from here Some of the terms that is B by two and here it should have been people as cuba too because many people ask you my toe. So this is B by two to a place T -1 in two D. Going to cuba to to a place Q minus one in two D. Okay so what we could do is just write me by Q to a place T -1 in today -62 to a place few miles when In two d. equal to zero. Okay so disappear to Pretty bad too. No it is take one x 2 common and we will be getting inside. Is uh ap miss to ap bless be a Squire minus P into D minus to a queue. We're multiplying this to a queue wow. And uh it will be minus Q. Esquire Q. A square. Lescure. Okay we should. All right. He says minus Q. S square and minus Q. Oh In today equal to zero. This is one x 2. Is it too happy to wake you? So if you take to a common it will become p minus Q. And this is square minus. Okay no problem. Let us stay D. Has common from this. So this will be equal to be a Squire minus b minus q. Square plus Q equal to zero. So this is one x 2 to a p minus Q equal to not a quarter plus D. And this is the square minus q square. This should be written as people ask you into b minus q and minus b minus Q. For these two equal to zero. So one x 2 to a p minus Q plus p minus Q should be taken as common, P minus Q in two D. Into B plus Q -1 equal to zero. Don't let us take b minus cuba is common. The p minus Q divided by two to a place. People sq minus one in today equal to zero. Okay, so it should have been people ask you here. Not B minus I think there is a mistake has to be okay. Not a problem. This can Britain is do it Plus people secure -1 day equal to zero. So we will be having as people skew equal to zero. Thank you.

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