Question

if the ratio of the sum of n terms of two AP's be (7n+1):(4n+27),then the ratio of their 11 th terms will be

Answer 1

Let sum of n terms of first A.P. be 7n+1 and second A.P be 4n +27
Taking the value of n =1 we get value of sum of first term that is first term of first A.P. as 7 and of second A.P. as 31
Taking the value of n=2 , we get value of sum of first two terms of first A.P. as 15 and second A.P. as 35
Second term= Sum of first two terms- First term
For 1st A.P., second term will be 15-7=8
For 2nd A.P., second term will be 35-31=4
Let first A.P. be 7,8 and Second A.P. be 31,35
So, for first A.P. eleventh term will be :
a+(n-1) d = 7+ (11-1) 1 = 7+10=17
So, for second A.P. eleventh term will be ;
a+(n-1) d = 31+(11-1) 4 = 31+40=71
So, ratio of 11th term of both A.P
is
$\frac{17}{71}$