let sum of first n term of two ap are in the ratio 2n+1/3n-1 . Find ratio of there 11 th term
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let sum of first n term of two ap are in the ratio 2n+1/3n-1 . Find ratio of there 11 th term
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2(a+(n-1/2)d) / 2(A+(n-1/2)D) = 5n+4/ 9n +6
(a+(n-1/2)d) / (A+(n-1/2)D) = 5n+4 / 9n+6. .....(I)
We have to find
a+17d / A+17 D
hence , n-1/2 = 17
n- 1 = 17 × 2
n -1 = 34
n= 34 +1
n= 35
putting n= 35 in (1)
(a+(35-1/2)d) / (A+(35-1/2)D) = 5(35) + 4/9 (35) +6
(a+(34/2)d) / (A+34/2)D) = 179/321
Therefore 18th term of 1st AP/18th term of 2nd AP =179/321
hence the ratio of 18th term of 1st AP and 18th term of 2nd AP is 179:321
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