Question

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

HERE IS UR ANSWER
if the ratio of the sum of two APs are 7n+1:4n+27
find ratio of their 9th term
then put n = 9 in both APs,
7×9+1:4×9+27
64:63
so the ratio's of their 9th term will be 64:63

Answer 2

Answer:24:19

Step-by-step explanation:

Let the first terms of the a.p s be A and a respectively

and the common differences of the two a.p s be D and d respectively

and let the the sum of firs n terms of the a.p s be Sn and Tn respectively

∴A.T.Q

Sn:Tn=(7n+1):(4n+27)

⇒{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)

putting (n=17) in the given equation we get

⇒(2A+16D)/(2a+16d)=120/95

⇒2(A+8D)/2(a+8d)=24/19

⇒(A+8D)/(a+8d)=24/19

⇒A+(9-1)D/a+(9-1)d=24/19

⇒A19/a19=24/19

∴Ratio of the 9th term of the two a.ps are 24:19