Integers a,b,c,d and e satisfy 50<a<b<c<e and a,b,c,d,e from a geometric sequence what is the sum of all possible distinct values of a?

Answer 1

No way to tell. All you have said is that 50<a.

I think there is something missing here.

Answer 2

Crazy question.
Agree with you, there has to be more
As it stands:

b/a = c/b and c/b = d/c and d/c = e/d
b^2 = ac , c^2 = bd , d^2 = ed
then b^2 c^2 d^2 = abcde

I then ran this "primitive" BASIC program

10 for a = 50 to 100
20 for b = 51 to 100
30 for c = 52 to 100
40 for d = 53 to 100
50 for e = 54 to 100
60 if (b*c*d)^2 = (a*b*c*d*e) then print a;b;c;d;e
70 next e
80 next d
90 next c
100 next b
110 next a

and got no output after about 6 million loops

Answer 3

I think I missed the obvious

Since a,b,c,d,e are integers in GS, the smallest value of r is 2
a - b - c - d - e
51 102 204 408 816
52 104 ...
53 ....

infinite number of choices for a
so...
still a silly question

Answer 4

Forget my previous post,
r could be 1.5

my program line 60 should say:
60 if (b*c*d)^2 = (a*b*c^2*d*e) then print a;b;c;d;e

and I got

64 96 144 216 324
80 120 180 270 405
96 144 216 324 486

Answer 5

The answer is 321. Possible values of a are:
64(r=1.5)
80(r=1.5)
81(r=4/3)
96(r=1.5)