the ratio of the sum of n and m terms of an a.p. is m square: n square. show that the ratio of the mth term and nth term is (2m - 1) : (2n -1)
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Sm/Sn=m^2/n^2 ============(1)
but we know Sn=n/2 {2a+(n-1) d }
hence we convert equation to formula form .
Sm/Sn=m^2/n^2=[m/2 {2.1+(m-1) 2}]/[n/2 {2.1+(n-1).2}]
now we see above we convert in standard form .
now if see
for n
a=1 and d =2
for m
a=1 and d=2
now
mth term/nth term ={a+(m-1) d}/{a+ (n-1) d}
=(1+2m-2)/(1+2n-2)
=(2m-1)/(2n-1)
but we know Sn=n/2 {2a+(n-1) d }
hence we convert equation to formula form .
Sm/Sn=m^2/n^2=[m/2 {2.1+(m-1) 2}]/[n/2 {2.1+(n-1).2}]
now we see above we convert in standard form .
now if see
for n
a=1 and d =2
for m
a=1 and d=2
now
mth term/nth term ={a+(m-1) d}/{a+ (n-1) d}
=(1+2m-2)/(1+2n-2)
=(2m-1)/(2n-1)
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7
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