Question

Thesum of n terms of a series in A.P. are in the ratio (3n-13):(5n+21). Find the ratio of their 24th terms.

Answer 1

=  Sn/Sn = 3 n-13/5 n+21

 n/2 (2 a + (n-1 ) d / n/2( 2 a +(n-1)d  =  3 n-13 / 5 n+21

  (2 a + (n-1 ) d / ( 2 a + (n-1) d =  3 n- 13 / 5 n+21

To find 24th terms Ratio

Replacing n = 47

(2 a + (47 -1 ) d / ( 2 a + (47 -1) d = 3* 47 - 13/ 5*47 +21

(2 a + 46d) / (2a + 46d)  =  141- 13 /  235+21

( a + 23d ) / (a + 23d ) = 128 / 256

(  a +(24-1)d ) / ( a +(24 -1 )d) =   1 / 2

Ratio of The 24th Term = 1 : 2