Question

A média aritmética simples entre 2^26, 2^27, 2^28 e 2^29 é igual a:
(A) 2^24
(B) 2^25
(C) 2^27,5
(D) 7 × 2^24
(E) 15 × 2^24

Answer 1

$\sf\underbrace{\sf\big\{x_1,x_2,x_3,x_4,\dots\big\}}_{y\:elementos}\implies M_s=\dfrac{x_1+x_2+x_3+x_4+\dots}{y}$

$\therefore$

$\sf\big\{2^{26},2^{27},2^{28},2^{29}\big\}\implies M_s=\dfrac{2^{26}+2^{27}+2^{28}+2^{29}}{4}$

$\sf M_s=\dfrac{2^{26}(2^{26}+2^{26+1}+2^{26+2}+2^{26+3})}{2^2}$

$\sf M_s=\dfrac{2^{26}(1+2^1+2^2+2^3)}{2^2}$

$\sf M_s=\dfrac{2^{26}(1+2+4+8)}{2^2}$

$\sf M_s=\dfrac{2^{26}\cdot15}{2^2}$

$\sf M_s=2^{26-2}\cdot15$

$\red{\sf M_s=2^{24}\cdot15}$

Letra E