The ratio of the sums of $m$ and $n$ terms of an A.P. is $m^{2}: n^{2}$. Show that the ratio of $m^{\text {th }}$ and $n^{\text {th }}$ term is $(2 m-1):(2 n-1)$.

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Precalculus

NCERT Class 11 - Math

Chapter 9

Sequences and Series

Section 2

Sequences

Discussion

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Video Transcript

following number 12. In which it is given that the issue of some of m and in terms of an ap the issue of some sort of eminent terms so they should have some of and in terms are given us uh mm squired by and squared. So we have to find the ratio of and okay I'm a german and it's strong, we have to show that Base to M -1 by To end -1. This we have to find out. So basically if we explore it it will be if A and D are the first time in commendation respectively, then a place M -1 D By a plus and -1 D Equal to -1 by two in -1. We have to prove it. Okay so basically we have to find these values get started from here. We can be we will be having mm bye too to a plus m minus one D. Equal to I am inspired by inspired over here and by two to a bless And uh -1 deep. Okay two and 2 will get cancelled out. We'll be having em and one more thing will be canceled out. This M and M will get cancelled out and we'll get canceled out. So basically we'll be having to a place M -1 d. Divide by to a place and minus one D. Equal to and by and okay what else we can do is this is to a okay To him by and to him -1 by to him this one. Okay Okay so if you're right it is to a place MD minus the Divide by two way place and G minus D. Going to M by N. And if you look at it it comes out to be M. D. List two A -D. divided by and Deep Bliss. Two A minus day equal to come by. And this is and Okay if you compare it will be having the equal to one D. Equal to one and two in minus the equal to zero. So to you minus the equal to zero which means they will be equal to 1x2. Now let us plug in the values over here and it is Caithness and -1 Day is one x 2. Plus M -1 in today is one divide by the elegance of this of the expression we have to prove one x 2. A plus And -1 in two d. Which means This is one x 2. Bless em minus one by one by two. Plus n minus one equal to to um minus one. And by two It will be to end mines one x 2. These two will get cancelled out. So we will be having two in -1 x two in -1. This is think we needed to prove. Thank you.

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