SOLUTION: Given the sequence -1,2,-4,8... What is the 10th term ? Write the number only

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Question 1035524: Given the sequence -1,2,-4,8... What is the 10th term ? Write the number only
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
From -1 to 2, we're multiplying by -2
From 2 to -4, we're multiplying by -2
From -4 to 8, we're multiplying by -2
and so on

The rule is this:
to get the next term, we multiply the previous term by -2

So the term after 8 is -16 because
8 times -2 = -16
and the term after -16 is 32 because
-16 times -2 = 32
etc etc

Let's generate up to the 10th term
Term NumberTermNotes
1-1Given
22Given
3-4Given
48Given
5-168*(-2) = -16
632-16*(-2) = 32
7-6432*(-2) = -64
8128-64*(-2) = 128
9-256128*(-2) = -256
10512-256*(-2) = 512


So the tenth term is 512

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Shortcut Method

First term is a = -1
Common ratio is r = -2

The nth term of this geometric sequence is a%2Ar%5E%28n-1%29+=+-1%2A%28-2%29%5E%28n-1%29

Plug in n = 10 to get



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Either way, the final answer is 512