To find the explicit formula for the given sequence, we can observe how the values change from one term to the next.
Starting with the first few terms:
- \( 1400 \) to \( 560 \): Divide by \( 2.5 \) (or multiply by \( \frac{2}{5} \))
- \( 560 \) to \( 224 \): Divide by \( 2.5 \) (or multiply by \( \frac{2}{5} \))
- \( 224 \) to \( 89.6 \): Divide by \( 2.5 \) (or multiply by \( \frac{2}{5} \))
- \( 89.6 \) to \( 35.84 \): Divide by \( 2.5 \) (or multiply by \( \frac{2}{5} \))
The pattern implies we are multiplying by \( \frac{2}{5} \) every time.
Therefore, the explicit formula for the sequence can be expressed as:
\[ a_n = 1400 \times \left( \frac{2}{5} \right)^{n-1} \]
In the form requested, the correct responses would be:
- an = 1400
- Response area(n−1)
- (2/5)
So the complete formula for the sequence is:
\[ a_n = 1400 \left( \frac{2}{5} \right)^{n-1} \]