Question

Vă rog frumos, din suflet, sa ma ajutați si pe mine la ex 4 si 5......

Answer 1

4.

$2*2^x-1-(2^x-1)=2^{x+1}+3-(2*2^x-1)$

$2^{x+1}-1-2^x+1=2^{x+1}+3-2^{x+1}+1$

$2^x*(2-1)=4$

$2^x=4$

$x=2$

5.

$a_3=5 ; r=2$

$a_1=a_3-2*r$

$a_1=1$

$a_n=a_1+(n-1)*r$

$a_n=1+(n-1)*2$

$a_n=2*n-1$

$a_1+a_2+...+a_n=400$

$1+3+...+2*n-1=400$

$\frac{2*n*\frac{2*n-1+1}{2}}{2}=400$

$\frac{n*2*n}{2}=400$

$n^2=400$

$n=20$