If n,6 M are in geometric sequence n,7.5, m are in arithmetic sequence ,then find the value of n and m?​

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:

with n = 12 => m = 3

       n = 3 => m = 12

=> (m;n) = {(3;12),(12;3)}

Step-by-step explanation:

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