Question

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

Answer 1

Please see the attachment

Answer 2

In 1st AP ,
Sn = 7n + 1
S9 = 7(9) + 1 = 64
S10 = 7(10) + 1 = 71
Therefore,
a9 = S10 - S9
a9 = 71 - 64 = 7........(1)

In 2nd AP,
Sn = 4n + 27
S9 = 4(9) + 27 = 63
S10 = 4(10) + 27 = 67
Therefore
a9 = S10 - S9
a9 = 67 - 63 = 4.......(2)

Thus, the ratio is about 7:4.

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