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) (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 Number | Term | Notes |
|---|
| 1 | -1 | Given |
| 2 | 2 | Given |
| 3 | -4 | Given |
| 4 | 8 | Given |
| 5 | -16 | 8*(-2) = -16 |
| 6 | 32 | -16*(-2) = 32 |
| 7 | -64 | 32*(-2) = -64 |
| 8 | 128 | -64*(-2) = 128 |
| 9 | -256 | 128*(-2) = -256 |
| 10 | 512 | -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
Plug in n = 10 to get
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Either way, the final answer is 512
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