Question

If the ratio of the sum of the first n terms of two A.P's is (7n+1):(4n+27),then find the ratio of there 9th terms?​

Answer 1

Answer:

hope it help's ^,^

Step-by-step explanation:

Let’s denote the sums of 2 AP’s as S1andS2,S1andS2,

Given that, S1S2=7n+14n+27,S1S2=7n+14n+27,

Sum of first ‘n’ terms of AP, whose first term is ‘a’ and common difference is ‘d’, is given by-

S=n2[2a+(n−1)d]S=n2[2a+(n−1)d]

Let,

First term and common difference of two AP’s having sum S1S1 and S2S2 be ‘a’ , ’d’ and ‘A’ , ‘D’ respectively.

Then, S1S2=n2[2a+(n−1)d]n2[2A+(n−1)D],S1S2=n2[2a+(n−1)d]n2[2A+(n−1)D],

=> S1S2=2a+(n−1)d2A+(n−1)DS1S2=2a+(n−1)d2A+(n−1)D

=> S1S2=a+n−12