Question

You buy a bag of skittles that contains 500 pieces of candy in it. Each day you eathalf of the amount that is in the bag.1. Geometric or Arithmetic and Why:2. Create a table that shows how many skittles are in the bag after 4 days3. Write an explicit and recursive formula for this sequence4. How many days will it take to where there is less than one skittle in the bag?

Answer 1

1) The data

Day 1: 500 skittles

Day 2: 1/2 eaten (250)

Day 3: 1 eaten (125)

Day 4 : 62.5 skittles

Day 5: 31.25

Day 6: 15.625

Day 7: 7.8125

2) This is a Geometric Sequence because there is a decrease of 1/2

500 * 1/2 = 250

250 *1/2 = 125

125*1/2=62.5

2) Table above on 1)

3) Let's write an explicit formula for that: You just need the first term and the ratio (q). In this case 1st term: 500 ratio (q) = 1/2

$\begin{gathered} a_n=a_1\cdot q^{n-1} \\ a_2=500.(\frac{1}{2})^{2-1} \\ a_2=250_{} \end{gathered}$

In a Recursive Formula, You have to know the prior term. You'll only find the second term if you know the first one. Like this:

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