Question

If ratio of the sum of first n terms of two A.P is 7n+1:4n+27,then find the ratio of their 9th terms.

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Answer 1

(n-1)/2 came because we divided both Numerator and denominator of left side by 2 . i hope it is clear for you now.

and we are giving (n-1)/2 =8 because all AP'S are of the form a+(n-1)d and in this case 9 term's ratio is to be found out . so (9-1) = 8 is used there.