7. A, B, C, and D are positive integers. A, B,C forms an arithmetic sequence while B, C, D forms a

geometric sequence. if = , what is the smallest possible value of A+B+C+D

Complete Question

The positive integers A, B, and C form an arithmetic sequence while the integers B, C, and D form a geometric sequence. If (C/B) = (5/3), what is the smallest possible value of A + B + C + D?

52

Step-by-step explanation:

If A, B, and C form an arithmetic progression

Their arithmetic mean,

2B=A+C

C= 2B-A

B, C, D forms a  geometric sequence and Common ratio, r=C/B=5/3

The terms in the geometric sequence are:

Therefore:

So:

From arithmetic sequence

Common difference,

These all have to be positive integers so B must be a multiple of 9, The smallest values are if B is 9

A,B,C,D=3,9,15,25

So the smallest possible value for:

A+B+C+D = 3+9+15+25 = 52

how am i supposed to answer

step-by-step explanation: