To find the explicit formula for the given sequence \(1400, 560, 224, 89.6, 35.84, \ldots\), we can first look for a pattern.
Let's analyze the ratios between consecutive terms:
- \( \frac{560}{1400} = \frac{2}{5} \)
- \( \frac{224}{560} = \frac{2}{5} \)
- \( \frac{89.6}{224} = \frac{2}{5} \)
- \( \frac{35.84}{89.6} = \frac{2}{5} \)
From above, we can see that each term of the sequence is obtained by multiplying the previous term by \( \frac{2}{5} \).
Starting with \( a_1 = 1400 \):
- \( a_2 = a_1 \cdot \frac{2}{5} \)
- \( a_3 = a_2 \cdot \frac{2}{5} = a_1 \cdot \left(\frac{2}{5}\right)^2 \)
- \( a_4 = a_3 \cdot \frac{2}{5} = a_1 \cdot \left(\frac{2}{5}\right)^3 \)
- Continuing this pattern, we have \( a_n = 1400 \cdot \left(\frac{2}{5}\right)^{n-1} \)
Thus, the explicit formula for the sequence is:
\[ a_n = 1400 \cdot \left(\frac{2}{5}\right)^{n-1} \]
So the response for the formula to complete is:
an = 1400 \cdot (2/5)^(n-1)
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