Question 1196057: Find the general rule of the sequence: 32, -16, 8, -4, ...
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Without more info, there could be infinitely many possible answers. See my previous post here for more details.
If we assume the sequence is geometric, then,
a = 32 = first term
r = -1/2 = common ratio
The idea is to multiply each term by -1/2
which leads to,
nth term = a*( r )^(n-1)
nth term = 32*( -1/2 )^(n-1)
Again this all hinges on the assumption we have a geometric sequence.
Let's check the answer with something like n = 3
a_n = 32*(-1/2)^(n-1)
a_3 = 32*(-1/2)^(3-1)
a_3 = 32*(-1/2)^(2)
a_3 = 32*(1/4)
a_3 = 8
We have 8 as the third term, which indeed matches with the given sequence. I'll let you check the other values.
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