Question

Ajutor va rog este in poza!​

Answer 1

Explicație pas cu pas:

a)

$A = 9 \cdot 2^{n+4} - 3 \cdot 2^{n+3} + 7 \cdot 2^{n+2} - 6 \cdot 2^{n+1} + 4 \cdot 2^{n} =$

$= 2^{n} \cdot (9 \cdot 2^{4} - 3 \cdot 2^{3} + 7 \cdot 2^{2} - 6 \cdot 2^{1} + 4)$

$= 2^{n} \cdot (9 \cdot 16 - 3 \cdot 8 + 7 \cdot 4 - 6 \cdot 2 + 4)$

$= 2^{n} \cdot (144 - 24 + 28 - 12 + 4)$

$= 2^{n} \cdot 140 = 2^{n} \cdot 5 \cdot 28 \implies \bf A \ \ \vdots \ \ 28$

b)

$A = 2^{n} \cdot 140 = 8960$

$2^{n} = 64 \iff 2^{n} = 2^{6} \\ \implies n = 6$