Question

ratio of the sum of n term of two ap is (7 n+ 1) :( 4 n + 27) find the ratio of their mth term

Answer 1

let a,A be the first terms and d,D be the common difference of two APs.
                    Sn1/Sn2=n/2[2a+(n-1)d]/n/2[2A+(n-1)D]
                                  =7n+1/4n+27
 2a+(n-1)d/2A+(n-1)D=7n+1/4n+27 
a+(n-1/2)d/A+(n-1/2)D=7n+1/4n+27
               putting,n-1/2=m-1
                                 n=2m-1
    a+(m-1)d/A+(m-1)D=7(2m-1)+1/4(2m-1)+27
                        am/Am=14m-6/8m+23 
 ratio=14m-6:8m+23
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