Question

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Answer 1

To find the ratio of there 9th term where n=9

So,

$\frac{(7n + 1)}{4n + 27}$

Putting the value of n as equal to 9 in the above ratio=

$\frac{7 \times 9 + 1}{4 \times 9 + 27} = \frac{64}{63}$

Therefore ratio =64:63

Answer 2

It is given that ,

7n+1/4n+27=S1/S2

➡7n+1/4n+27= n/2 [2a+(n-1)d] upon n/2 [2a+(n-1) d ]

cancelling n/2 from the second side we get,

➡7n+1/4n+27=2a+(n-1) d /2a+(n-1)d

By taking 2 as common the equation will be

7n+1/4n+27=a+(n-1)d/a+(n-1)d... (1)

Now , according to the question,

a9= a+(9-1)d

=(n−1)2=8

∴n−1=16

∴n=17

Now put the value of n in (1),

➡7(17)+1/4 (17)+1=a+8d/a+8d

➡120/95=a+8d/a+8d

➡24/19=a+8d/a+8d

hence.

Hope it helps you