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?​

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

Answers ( )

    0
    2021-08-31T02:01:47+00:00

    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:

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )