In an A.P. with first term a and common difference d ( a , d  = 0 ) , the ratio α of the sum of the first n terms to the sum of n terms succeeding them does not depend on n . Then the ratio d a and

Question

In an A.P. with first term a and common difference d ( a , d  = 0 ) , the ratio α of the sum of the first n terms to the sum of n terms succeeding them does not depend on n . Then the ratio d a ​ and the ratio α , respectively, are

TestHub · Accepted Answer

α = 2 n ​ ( 2 ( a + n d ) + ( n − 1 ) d ) 2 n ​ ( 2 a + ( n − 1 ) d ) ​ = 2 a − d + 3 n d 2 a − d + n d ​ . This is independent of n only if d = 0 (rejected) or 2 a − d = 0 . So d a ​ = 2 1 ​ and α = 3 1 ​ .

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