Answer:
if n,6,m are in geometric sequence
=> 6/n = m/6
⇔ mn = 36 (1)
if n,7.5, m are in arithmetic sequence
=> 7.5 - n = m - 7.5
<=> m + n = 15 (2)
from (1)(2), we have the equations:
[tex]\left \{ {{mn=36} \atop {m+n=15}} \right.\\\\<=>\left \{ {{mn=36} \atop {m=15-n}} \right.\\\\<=>\left \{ {{(15-n)n=36} \atop {m=15-n}} \right.\\\\<=>\left \{ {{n^{2}-15n+36 =0} \atop {m=15-n}} \right.\\\\<=>\left \{ {{n=12orn=3} \atop {m=15-n}} \right.[/tex]
with n = 12 => m = 3
n = 3 => m = 12
=> (m;n) = {(3;12),(12;3)}
Step-by-step explanation:
