The sums of n terms of two arithmetic series are in ratio of 2n+1:2n-1. Find the ratio of their 10th terms.

1 answer

Let n=19. Then we have

a1+a19 = a1+a1+18d = 2(a1+9d) = 2a10
b1+b19 = 2b10

Now, using the sum ratio,
(a1+a19)/(b1+b19) = a10/b10 = (2*19+1)/(2*19-1) = 39/37