Question

Sa se determine primii doi termeni ai progresiei geometrice bn daca:b8=256, q=4

Answer 1

$\displaystyle b_8=256,~q=4 \\ b_8=256 \Rightarrow b_1 \cdot 4^{8-1} =256 \Rightarrow b_1 \cdot 4^7=256 \Rightarrow b_1 \cdot 4^7=4^4 \Rightarrow \\ \Rightarrow b_1=4^4:4^7 \Rightarrow b_1=4^{4-7} \Rightarrow b_1=4^{-3} \Rightarrow b_1= \frac{1}{4^3}\Rightarrow \boxed{b_1= \frac{1}{64 }} \\ b_2=b_1 \cdot 4^{2-1} \Rightarrow b_2=b_1 \cdot 4^1 \Rightarrow b_2= \frac{1}{64} \cdot 4 \Rightarrow b_2= \frac{4}{64} \Rightarrow \boxed{b_2= \frac{1}{16} }$