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The ratio of the sums of m and n terms o...

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^(th)` and `n^(th)` term is (2m-1) : (2n -1) .

Text Solution

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`((m)/(2)[2a+(m-1)d])/((n)/(2)[2a+(n-1)s])=(m^(2))/(n^(2))rArr(2a+(m-1)d)/(2a+(n-1)d)=(m)/(n)`
`rArr2an+n(m-1)d=2am+m(n-1)d`
`rArr2a(n-m)=[mn-m-mn+n]d`
`rArr2a(n-m)=(n-m)drArrd=2a`
`therefore(T_(m))/(T_(n))=(a+(m-1)d)/(a+(n-1)d)=(a+(m-1)2a)/(a+(n-1)2a)=(a[1+(m-1)2])/(a[1+(n-1)2])=(2m-1)/(2n-1)`
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