Question

The ratio of the sums of m and n terms of an AP is m²:n². Find the ratio of m,th and n,th term

Answer 1

Sm/Sn = m/2 ( 2a + ( m-1)d))/ n/2 ( 2a + (n-1)d))

= m/n ( 2 a + (m-1)d) / ( 2a+ ( n-1) d) = m^2/n^2

2an + mdn -dn = 2am + nmd - dm

2an - dn = 2am - dm

2a( n-m) = -dm + dn = d( n-m)

2a = d


So am / an = a + ( m-1)d)/ a + (n-1) d)

= a + md - d )/ a + nd - d

= a + 2am - 2a) / a + 2an - 2a

= 1 + 2m - 2) / 1 + 2n - 2

= -1 + 2m )/ -1 + 2n