Question

the ratio of their sum of m and n term of ap is m^2: n^2. show that the ratio of their mth and nth term is 2m-1:2n-1
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Answer 1

Sm/Sn=m^2/n^2
m/2{2a+(m-1)d}/n/2{2a+(n-1)d}=m^2/n^2
2a+(m-1)d/2a+(n-1)d=m/n
2a+md-d=m. 1
2a+nd-d=n. 2
1-2
(m-n)d=(m-n)
d=1
Putting d=1 in eq. 1
2a+m-1=m
a=1/2
Am/An=a+(m-1)d/a+(n-1)d
Am/An=1/2+(m-1)1\1/2+(n-1)1
Am/An=1/2+m-1\1/2+n-1
Am=1+2m-2/2
Am=2m-1
An=1+2n-2/2
An=2n-1
Am/An=2m-1/2n-1