Question

Помогите)))
найдите $x_{10} ,$, если $x_{1}$, = √2 ,q= -√2

Answer 1

Геометрическая прогрессия

$b_{n}= b_{1}*q^{n-1} ⇒   x_{10}= x_{1}*q^{10-1}$

$x_{10}= sqrt{2}*{( -sqrt{2})}^{10-1}= sqrt{2}* {(-sqrt{2})}^{9}=- (sqrt{2}) ^{10}=- (sqrt{2}) ^{2*5}=- 2^{5}=$=32