Question

let sum of first n term of two ap are in the ratio 2n+1/3n-1 . Find ratio of there 11 th term ​

Answer 1

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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