Mértani sorozat – feladatok

Az alábbi mértani sorozatoknak megadtuk néhány adatát. Számítsd ki a kérdéses adatokat!

1. a₁ = 8;          q = 2;          n = 13;
   a_n = ?          S_n = ?

   a₁₃ = 32.768 = 2¹⁵;          S₁₃ = 65.528

   
   

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2. a₁ = 3;          q = 5;          n = 10;
   a_n = ?          S_n = ?

   a₁₀ = 5.859.375;          S₁₀ = 7.324.218

   
   

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3. a₁ = 5;          q = −4;          n = 8;
   a_n = ?          S_n = ?

   a₈ = −81.920;          S₈ = −65.535

   
   

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4. a₁ = −2;          q = 3;          n = 6;
   a_n = ?          S_n = ?

   a₆ = −486;          S₆ = −728

   
   

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5. a₁ = −1;          q = 6;          n = 8;
   a_n = ?          S_n = ?

   a₈ = −279.936;          S₈ = −335.923

   
   

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6. a₁ = 4;          q = −2;          a_n = 9;
   n = ?          S_n = ?

   a₉ = 1024 = 2¹⁰          S₉ = 684

   
   

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7. a₂ = 10;          q = 2;          n = 6;
   a₁ = ?          a_n = ?          S_n = ?

   a₁ = 5;          a₆ = 160;          S₆ = 315

   
   

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8. a₃ = 6;          a₇ = 54;
   a₁ = ?          q = ?          S₁₀ = ?

   a₁ = 2;          q = ±√3          S₁₀ ≈ 661,16 illetve S₁₀ ≈ 177,16

   
   

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9. a₃ = 27;          a₇ = 91,125;
   a₁ = ?          q = ?          S₅ = ?

   a₁ = 12;          q = 1,5;          S₅ = 158,25

   
   

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10. a₂ = 64;          a₇ = 2
    a₁ = ?          q = ?
    Tagja-e a sorozatnak a 256? Tagja-e a sorozatnak a 0,25?

    q = 1/2;          a₁ = 128
    A 256 nem tagja, mert egy sorozatnak nincs −1-edik tagja.
    A 0,25 a 10. eleme a sorozatnak.

    
    

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