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

Question

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

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1 year 2021-08-31T02:00:39+00:00 1 Answers 23 views 0

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:

$$\left \{ {{mn=36} \atop {m+n=15}} \right.\\\\<=>\left \{ {{mn=36} \atop {m=15-n}} \right.\\\\<=>\left \{ {{(15-n)n=36} \atop {m=15-n}} \right.\\\\<=>\left \{ {{n^{2}-15n+36 =0} \atop {m=15-n}} \right.\\\\<=>\left \{ {{n=12orn=3} \atop {m=15-n}} \right.$$

with n = 12 => m = 3

n = 3 => m = 12

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

Step-by-step explanation: