If the sums of n terms of two arithmetic progressions are in the ratio 3n+5/5n +7, then their nth terms are in the ratio ​

Question

If the sums of n terms of two arithmetic progressions are in the ratio \(\frac{3n + 5}{5n + 7}\), then their nth terms are in the ratio

A. \(\frac{3n -1}{5n -1}\)

B. \(\frac{3n +1}{5n + 1}\)

C. \(\frac{5n + 1}{3n +1}\)

D. \(\frac{5n -1}{3n -1}\)

Answer 1

The sums of n terms of two A.P`s are in ratio \(\frac{3n + 5}{5n +7}\)

Let a₁ and d₁ be the first term and common difference of the first A.P, respectively. Similarly let a₂ and d₂ be the common difference of the second A.P, respectively. According to the given condition.

 

Now the Nth term is given by a + (N–1) d Equating the coefficients

\(\frac{(n-1)}{2}\) = N -1

⇒ n = 2N – 1