Question

Sa se determine primii doi termeni ai progresiei geometrice ( b indice n ) daca:

a) b indice 8=256 , q=4

Answer 1

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