Question

Îmi poate explica și mie cineva cum se rezolva acest exercițiu? ​

Answer 1

Răspuns:

a)

Explicație pas cu pas:

$a_1^2+a_2^2+\cdots + a_n^2 = \frac{n(4n^2 - 1)}{3}\\Daca\: n = 1 \implies a_1^2 = \frac{1(4\cdot 1^2 - 1)}{3} = \frac{1\cdot 3}{3} = 1\implies a_1=\sqrt{1}\implies a_1 = 1\\\\Daca \:n = 2 \implies a_1^2 + a_2^2 = \frac{2(4\cdot 2^2-1)}{3}\\\\ 1 + a_2^2 = \frac{2(4^2-1)}{3}\\\\ 1+a_2^2 = \frac{2\cdot 15}{3} = 2\cdot 5 = 10\\\\ a_2^2 = 10 - 1\\\\ a_2^2 = 9\implies a_2 = \sqrt{9} = 3\\\\r = 3 - 1 = 2$

$Verificare:\\\\ n = 3\Rightarrow 1 + 9 + a_3^2 = \frac{3(4\cdot 3^2 - 1)}{3}\\\\10 + a_3^2 = 4\cdot 9 - 1\\\\ 10+a_3^2 = 35\\\\ a_3^2 = 25\\\\ a_3 = \sqrt{25} = 5\\\\a_2 = \frac{a_1 + a_3}{2}\\\\ 3 = \frac{1 + 5}{2} = \frac{6}{2} = 3\\\\Adevarat$