Question

scrieti primii sase termeni ai sirului(c↓n)definit in mod recurent c↓1=2,c↓2=1,c↓n+1=2c↓n-1

Answer 1

$\it c_1=2, \ \ c_2 = 1,\ \ \ c_{n+1}=2c_{n-1}$

$\it n=2 \Rightarrow c_{2+1}=2c_{2-1} \Rightarrow c_3 = 2\cdot c_1 \Rightarrow c_3 = 2\cdot 2 \Rightarrow c_3 = 4$

$\it n=3 \Rightarrow c_{3+1}=2c_{3-1} \Rightarrow c_4 = 2\cdot c_2 \Rightarrow c_4 = 2\cdot 1 \Rightarrow c_4 = 2$

$\it n=4 \Rightarrow c_{4+1}=2c_{4-1} \Rightarrow c_5 = 2\cdot c_3 \Rightarrow c_5 = 2\cdot 4 \Rightarrow c_5 = 8$

$\it n=5 \Rightarrow c_{5+1}=2c_{5-1} \Rightarrow c_6 = 2\cdot c_4 \Rightarrow c_6 = 2\cdot 2 \Rightarrow c_6 = 4$