To determine the 10th term of the sequence 8, 40, 200, ... we first need to identify the pattern of the sequence.
Let's look at how each term relates to the previous one:
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The second term (40) divided by the first term (8) is: \[ \frac{40}{8} = 5 \]
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The third term (200) divided by the second term (40) is: \[ \frac{200}{40} = 5 \]
It appears that each term is multiplied by 5 to get the next term. So, this is a geometric sequence where the first term \( a = 8 \) and the common ratio \( r = 5 \).
The formula for the nth term of a geometric sequence is given by: \[ a_n = a \cdot r^{(n-1)} \] where:
- \( a \) is the first term,
- \( r \) is the common ratio,
- \( n \) is the term number.
To find the 10th term (\( a_{10} \)): \[ a_{10} = 8 \cdot 5^{(10-1)} = 8 \cdot 5^9 \]
Now, we calculate \( 5^9 \): \[ 5^9 = 1953125 \]
Now we can substitute back to find \( a_{10} \): \[ a_{10} = 8 \cdot 1953125 = 15625000 \]
Thus, the 10th term is: \[ \boxed{15625000} \]
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