The sum of the first three terms of an AP is 30 and the ratio of second and the third number is 2:3. Then the ratio of the first and the third number is *

The sum of the first three terms of an AP is 30 and the ratio of secon

1.	The sum of the first three terms of an AP is 30 and the ratio of second and the third number is 2:3. Then the ratio of the first and the third number is *
Answer» From the question, it is given that, the SUM of three numbers in A.P. =30 The ratio of the first number to the third number is 3: 7Let US assume the 3 numbers which are in A.P. are, a−d,a,a+dNow adding 3 numbers =a−d+a+a+d=303a=30a=30/3a=10 Given ratio 3:7=a−d:a+d3/7=(a−d)/(a+d)(a−d)7=3(a+d)7a−7d=3a+3d7a−3a=7d+3d4a=10d4(10)=10d40=10dd=40/10d=4 THEREFORE, the numbers are a−d=10−4=6a=10a+d=10+4=14So,6,10,14,… are in A.P.