To find the missing number in the sequence –6, ____, –216, –1,296, –7,776, let's look for a pattern.
We can start by checking the ratios between consecutive terms:
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From –6 to –216: \[ \text{If we divide –216 by –6, we have: } \frac{-216}{-6} = 36. \]
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From –216 to –1,296: \[ \text{Now, } \frac{-1,296}{-216} = 6. \]
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From –1,296 to –7,776: \[ \frac{-7,776}{-1,296} = 6. \]
Now we can see that each number seems to be multiplied by a factor:
- The first step is multiplying by 36 (from –6 to –216).
- The subsequent steps involve multiplying by 6.
Next, we can work backwards to find the missing number. Starting from –216:
- To find the previous number before –216, we divide: \[ \frac{-216}{6} = -36. \]
So, the missing number in the sequence is –36.
The complete sequence is: –6, –36, –216, –1,296, –7,776.