The ratio of the sum of first n terms of two AP's is 7n+1:4n+27. Find the ratio of their 11th terms .
Ans: Let a_{1}, a_{2}... and d_{1}, d_{2} be the I terms are Cd's of two AP's.
Sn of one AP = 7n+1/4n+27
Sn of II AP
m/2[2a_{1} +(n-1)d_{1}]/ m/2 [2a_{2} +(n-1)d_{2}] = 7n+1/4n+27
ð 2a_{1} +(n-1)d_{1}/ 2a_{2} +(n-1)d_{2} = 7n+1/4n +27
ð We have sub n = 21
ð 2a_{1} +20d_{1}/2a_{2} +20d_{2} = 7 x21 + 1/4(21)+27
ð A_{1} +10d_{1}/a_{2} +10d_{2} = 148 /111
ð = 4/3