Question

The ratio of sums of m and n terms of an ap is m square : n square. Then prove that the ratio of mth and mth term of the ap is (2m-1):(2n-1).

Answer 1

Here's your answer hope it helps.

Answer 2

Answer:

LET A BE THE FIRST TERM AND D THE COMMON DIFFERENCE OF THE GIVEN AP.THEN,THE SUMS OF THE MTH TERM AND NTH TERM IS GIVEN BY.......

Sm=m/2{2a+m-1}d

Sn =n/2{2a+n-1}d

Sm/Sn=m²/n²

m/2{2a+m-1}d÷n/2{2a+n-1}d=m²/n²

{2a+m-1}d÷{2a+n-1}d=m/n

({2a+m-1}d)n=({2a+n-1}d)m

2a(n-m)=d{(n-1)m-(m-1)n}

2a(n-m)=d(n-m)

d=2a

Tm/Tn=a+(m-1)d÷a+(n-1)d

          = a+(m-1)2a÷a+(n-1)2a

          = 2m-1÷2n-1

hope it helps you!!!!!!