Question

what are the first 5 terms of the sequence where a=1 a, a2=2 and an=1/2(a n-1•a n-2)




a= 1,2,1,1,1/2
b= 1,2,4,8,16
c= 1,2,1, 1/2, 1/4
d= 1,2,4,4,8

Answer 1

Answer:

$\large\boxed{a.\ 1,\ 2,\ 1,\ 1,\ \dfrac{1}{2}}$

Step-by-step explanation:

We have the recursive formula of a sequence:

$\left\{\begin{array}{ccc}a_1=1\\a_2=2\\a_n=\dfrac{1}{2}(a_{n-1}\cdot a_{n-2})\end{array}\right\\\\\text{thereofre}\\\\a_3=\dfrac{1}{2}(a_2\cdot a_1)=\dfrac{1}{2}(2\cdot1)=\dfrac{1}{2}(2)=1\\\\a_4=\dfrac{1}{2}(a_3\cdot a_2)=\dfrac{1}{2}(1\cdot2)=\dfrac{1}{2}(2)=1\\\\a_5=\dfrac{1}{2}(a_4\cdot a_3)=\dfrac{1}{2}(1\cdot1)=\dfrac{1}{2}(1)=\dfrac{1}{2}$