Comparte esto 👍👍
CAPITULO XXXVII

Progresiones Geométricas
Ejercicio 294
Interpolar:
  1. 3 medios geométricos entre 5 y 3125.
    Sea: a=5,u=3125,n=5 ÷ ÷ 5…………………3125 r = u a n1 r = 5 51 r = 6254 r = 5 4 4 r = ± 5 5 × ± 5= ± 25 25 × ± 5= ± 125 125 × ± 5= ± 625 ÷ ÷ 5: ± 25: ± 125: ± 625:3125
  2. 4 medios geométricos entre -7 y -224.
    Sea: a=7,u=224,n=6 ÷ ÷ 7…………………224 r = u a n1 r = 7 61 r = 325 r = 2 5 5 r =2 7 × 2=14 14 × 2=28 28 × 2=56 56 × 2=112 ÷ ÷ 7:14:28:56:112:224
  3. 5 medios geométricos entre 128 y 2.
    Sea: a=128,u=2,n=7 ÷ ÷ 128…………………2 r = u a n1 r = 2 71 r = 1 64 6 r = 1 2 6 6 r = ± 1 2 128( ± 1 2 ) = ± 64 64( ± 1 2 ) = ± 32 32( ± 1 2 ) = ± 16 16( ± 1 2 ) = ± 8 8( ± 1 2 ) = ± 4 ÷ ÷ 128: ± 64: ± 32: ± 16: ± 8: ± 4:2
  4. 4 medios geométricos entre 4 1 2 y 16 27 .
    Sea: a= 9 2 ,u= 16 27 ,n=6 ÷ ÷ 9 2 ………………… 16 27 r = u a n1 r = 16 27 9 2 61 r = 2 4 3 3 3 2 2 5 r = 2 5 3 5 5 r = 2 3 9 2 × 2 3 =3 3 × 2 3 =2 2 × 2 3 = 4 3 4 3 × 2 3 = 8 9 ÷ ÷ 9 2 :3:2: 4 3 : 8 9 : 16 27 ÷ ÷ 4 1 2 :3:2:1 1 3 : 8 9 : 16 27
  5. 6 medios geométricos entre 2 y 34 11 64 .
    Sea: a=2,u= 2187 64 ,n=8 ÷ ÷ 2………………… 2187 64 r = u a n1 r = 2187 64 2 81 r = 2187 128 7 r = 3 7 2 7 7 r = 3 2 2 × 3 2 =3 3 × 3 2 = 9 2 9 2 × 3 2 = 27 4 27 4 × 3 2 = 81 8 81 8 × 3 2 = 243 16 243 16 × 3 2 = 729 32 ÷ ÷ 2:3: 9 2 : 27 4 : 81 8 : 243 16 : 729 32 : 2187 64 ÷ ÷ 2:3:4 1 2 :6 3 4 :10 1 8 :15 3 16 :22 25 32 :34 11 64
  6. 4 medios geométricos entre 4 9 y 27 256 .
    Sea: a= 4 9 ,u= 27 256 ,n=6 ÷ ÷ 4 9 ………………… 27 256 r = u a n1 r = 27 256 4 9 61 r = 3 3 4 4 4 3 2 5 r = 3 5 4 5 5 r = 3 4 4 9 × 3 4 = 1 3 1 3 × 3 4 = 1 4 1 4 × 3 4 = 3 16 3 16 × 3 4 = 9 64 ÷ ÷ 4 9 : 1 3 : 1 4 : 3 16 : 9 64 : 27 256
  7. 7 medios geométricos entre 8 y 1 32 .
    Sea: a=8,u= 1 32 ,n=9 ÷ ÷ 8………………… 1 32 r = u a n1 r = 1 32 8 91 r = 1 2 5 2 3 8 r = 1 2 8 8 r = ± 1 2 8( ± 1 2 ) = ± 4 4( ± 1 2 ) = ± 2 2( ± 1 2 ) = ± 1 1( ± 1 2 ) = ± 1 2 1 2 ( ± 1 2 ) = ± 1 4 1 4 ( ± 1 2 ) = ± 1 8 1 8 ( ± 1 2 ) = ± 1 16 ÷ ÷ 8: ± 4: ± 2: ± 1: ± 1 2 : ± 1 4 : ± 1 8 : ± 1 16 : ± 1 32