If the sums of n terms of two arithmetic progressions are in the ratio , then their nth terms are in the ratio

The sums of n terms of two A.P`s are in ratio

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}

⇒ n = 2N – 1

= = =