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

`\large\boxed{a.\ 1,\ 2,\ 1,\ 1,\ (1)/(2)}`

Explanation:

We have the recursive formula of a sequence:

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