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A sequence is shown.

1400, 560, 224, 89.6, 35,84,.....

Complete the explicit formula for the sequence.

(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
an=
Response area. Response area(n−1)
(1400, 35.84, 2/5, or 5/2)

1 answer

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:

  1. an = 1400
  2. Response area(n−1)
  3. (2/5)

So the complete formula for the sequence is:

\[ a_n = 1400 \left( \frac{2}{5} \right)^{n-1} \]