In a set of four numbers the first three are in G.P. and  the last three are in A.P. with a common difference 6.  If the first number is same as the fourth, the four numbers are

Let the last three numbers in A.P. be b, b + 6, b + 12 and the first number be a.Hence the four numbers are a, b, b + 6, b + 12Given,  a=b+12                                (1)and a, b, b + 6 are in G.P. i.e., b2 = a (b + 6)or       b2 = (b + 12) (b + 6)        (∴a = b + 12) or  18b = – 72 \ b = –4,From Eq. (1),a = – 4 + 12 = 8.Hence, the four numbers are 8, –4, 2 and 8.