Question

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

Answer 1

hope it will help you

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let a, d and A, D be the 1st term and common difference of two given APs.

Then,

We know that,

S(n) = n/2[2a + (n - 1)d]

⇒ {n/2[2a + (n - 1)d]/n/2[2A + (n - 1)D]} = 7n + 1/4n + 27

⇒ 2a + (n - 1)d/2A + (n -1)D = 7n + 1/4n + 27

Replacing n by 17 in both L.H.S and R.H.S, we get

⇒ 2a + (17 - 1)d/2A + (17 - 1)D = 7(17) + 1/4(17) + 27

⇒ 2a + 16d/2A + 16D = 119 + 1/68 + 27

⇒ 2(a + 8d)/2(A + 8D) = 120/95

We know that

a + (n - 1)d = a(n)

⇒ a(9)/A(9) = 24/19

Hence, the ratio of 9th term is 24 : 19.

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