Question
Mathematics Question on Exponential and Logarithmic Functions
The sum of n terms of two AP's are in the ratio of (3n+8):(7n+15). Find the ratio of their 12th terms.
A
(A) 712
B
(B) 167
C
(C) 716
D
(D) 127
Answer
(C) 716
Explanation
Solution
Explanation:
Let us consider two AP's having first term a1 and a2 and the common difference are d1 and d2 respectively.According to the question,S1 S2=3n+87n+15Sum of the first n terms =Sn=n2[2a+(n−1)×d]n2[2a1+(n−1)d1)]n2[2a2+(n−1)d2)]=3n+87n+15[a1+(n−12)d1)][a2+(n−12)d2]=3n+87n+15So, the ratio of 12th term of both AP is:a1+11d1a2+11d2=[a1+(n−12)d1)][a2+(n−12)d2]=3n+87n+15So, we can write n−12=11Therefore,n=23So,a1+11 d1a2+11 d2=3×23+87×23+15=77176=716Hence, the correct option is (C).