Question

Write out the first 5 terms of the following sequence:

Answer 1

9514 1404 393

Answer:

2, 1, -1/2, -1/4, 1/8

Explanation:

Use n = 1 through 4:

`a_(1+1)=((-1)^(1+1)\cdot a_1)/(2)\ \Rightarrow\ a_2=(1\cdot2)/(2)=1\\\\a_3=((-1)^3\cdot 1)/(2)=-(1)/(2)\\\\a_4=((-1)^4\cdot(-(1)/(2)))/(2)=-(1)/(4)\\\\a_5=((-1)^5\cdot(-(1)/(4)))/(2)=(1)/(8)`

The first 5 terms are ...

2, 1, -1/2, -1/4, 1/8