Question

Another sequence. The fractions are throwing me off

1,-1/2,1/4

Answer 1

This is a geometric sequence. Do you know why?

Answer 2

I forgot

Answer 3

A geometric sequence is a sequence of numbers you can use a common factor (something you multiply by) to get the next number.
Lets start with what you multiply 1 by to get -1/2. Do you know?

Answer 4

Well, if you don't, think of it like this. Dividing by 2 is the same as multiplying by 1/2. 1 times 1/2 = 1/2. Now make that negative. 1*-1/2=-1/2

Answer 5

Also, a negative times a negative equals a positive so -1/2*-1/2= +1/4

Answer 6

So the recursive formula for this sequence is A(n)=A(n-1)(-1/2)

Answer 7

and A(1)= 1

Answer 8

I think a faster way of getting the key formula would be (-1)^n 1/2^n

Answer 9

so if we let n = 1
(-1)^1 1/2^1 then it's -1/2
n = 2
(-1)^2 1/2^2 = 1/4 and so on and so on

Answer 10

the pattern is positive negative positive negative... so we start at n = 0

Answer 11

you need this === > (-1)^n 1/2^n and let n = 0., 1, 2, ....

Answer 12

Ah ok