The sum of each of two sets of three terms in A.P. is 15. The common difference of the first set is greater than that of the second by 1 and the ratio of the products of the terms in the first set and that of the second set is 7:8 the ratio of the smallest terms in two sets of terms is
34 or 1112
Let the first set of number be a−d,a,a+d.
Then a−d+a+a+d=15⇒a=5
The second set of numbers will be
b−(d−1),b,b+(d−1).Again,b−(d−1)+b+b+(d−1)=15⇒b=5
Hence the sets of numbers are
5−d,5,5+d and 6−d,5,4+d.
Further, from the given condition
(5−d)5(5+d)(6−d)5(4+d)=78⇒25−d224+2d−d2=18
⇒d2+14d−32=0⇒d=2,−16
∴ the two sets are 3,5,7 and 4,5,6 or 21,5,−11 and 22,5,−12.
∴ Ratio of their smallest term is
34 or −11−12i.e.34 or 1112