Question

For each sequence write an explicit formula 96,48,24,12,6

Answer 1

`a_1=96;\ a_2=48;\ a_3=24;\ a_4=12;\ a_5=6\\\\a_1=a_2:2\to96:2=48\\a_2=a_3:2\to48:2=24\\a_3=a_2:2\to24:2=12\\a_4=a_3:2\to12:2=6\\\\therefore\\\\a_n=96:2^(n-1)=\frac {96}{2^(n-1)}\\\\check:\\a_1=(96)/(2^(1-1))=(96)/(1^0)=96\\a_2=(96)/(2^(2-1))=(96)/(2^1)=(96)/(2)=48\\a_3=(96)/(2^(3-1))=(96)/(2^2)=(96)/(4)=24\\\vdots`