Question

Three numbers form a geometric sequence. Their sum is 21 and their product is 64. Find the numbers(please show working)

Answer 1

a,b,c\[S_n=\frac{ a(1-r^n) }{ 1-r }\]
\[\frac{ T_2 }{ T_1 }=\frac{ T_3 }{ T_2 }\]

Answer 2

So from here how do I continue this is what I've tried so far and it's not getting me anywhere:
(T2/T1)=(b/a)r and (T3/T2)=(c/b)r

Answer 3

b/a=c/b
b^2=ac

Answer 4

so we have\[a+b+c=21\]
\[abc=64\]
\[b^2=ac\]
3 equations 3 unknowns ,solve

Answer 5

u can easily find b from
abc=64 and b^2=ac

Answer 6

try it, if u can't i'll help u

Answer 7

k, an trying this out now
already got b=4

Answer 8

thats correct, now u know how u can get a,c ?

Answer 9

just got it, a=1,b=4,c=16 thanks alot!