Question

How is n=2m-1 while finding ratio of mth term of two AP.s ?


prove it in details.



NO SPAMMING​

Answer 1

Given :

Now sum of n th terms of the A.P  is :

( 7 n + 1 ) : ( 4 n + 26 )

So :

Let our first term be a1 and a2 for the A.Ps

Let the differences be d1 and d2 .

After simplifying we will get :

[ a1 + ( n - 1 )/2 d1 ] / [ a2 + ( n - 1 )/2 d2 ]

Now put ( n - 1 )/2 as m - 1 so as to get the answer :

n - 1 = 2 m - 2

⇒ n = 2 m - 1

Hence n = 2 m - 1

Thus we get :

m th term ratios = [ 7 ( 2m - 1 ) + 1 ] / [ 4 ( 2m - 1 ) + 26 ]

⇒ [ 14 m - 6 ] : [ 8 m + 22 ]