Question

if the ratio of first n terms of two AP's is (7n+1) : (4n+27) find the ratio of their mth terms , plz answer guys ,it is much appreciated

Answer 1

Heya !!

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Given that, s/S = (7n+1) / (4n+27)

Let a, d and A, D be the first terms and common difference of two A.P.s.

s / S = { n/2 [ 2a + (n-1)d ] } / { n/2 [ 2A + (n-1)D ] }

=> s / S = [ 2a + (n-1)d ] / [ 2A + (n-1)D ]

=> s / S = { a + [(n-1)d / 2] } / { A + [(n-1)D/ 2] } .....(1)

Now, an = a+(n-1)d

Thus, mth term of the two A.P.s having s and S will be

a / A = [ a + (m-1)d ] / [ A + (m-1)D ] .....(2)

From equations (1) and (2)
we get 2m-1


Replacing n by 2m – 1 in both LHS and RHS.

[ 2a + (2m-1-1)d ] / [ 2A + (2m-1-1)D ] = [ 7(2m-1) + 1 ] / [ 4(2m-1) + 27 ]

=> [ a + (m-2)d ] / [ A + (m-2)D ] = (14m – 6) / (8m + 23)

Hence the ratio of the A.P.s is (14m – 6) : (8m + 23)

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Hope my ans.'s satisfactory.☺

Answer 2

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