Question

Wyznacz czwarty wyraz ciagu geometrycznego [tex]\sqrt{2} , 4-\sqrt{2}[/tex], ......

Answer 1

Odpowiedź:

[tex]a_1 = \sqrt{2} \\a_2 = 4 - \sqrt{2}[/tex]

q = [tex]a_2 : a_1 = 2\sqrt{2}- 1[/tex]

więc

[tex]a_4 = a_2*q^2 = ( 4 - \sqrt{2})*(2\sqrt{2} - 1)^2 = ( 4 - \sqrt{2})*(9 - 4\sqrt{2} ) =[/tex]

    = 36 - 16 √2 - 9 √2 + 8 = 44 - 25 √2

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Szczegółowe wyjaśnienie:

( 2√2 - 1 )² = 4*2 - 2*2√2*1 + 1 = 9 - 4 √2