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3.2.1: Sequences As Functions

http://walch.com/wu/CAU3L2S1Greenhouse

Sophia has a greenhouse. She’s trying to grow a demanding species of orchid that requires water every 3 days—no more, no less. The first day Sophia waters the orchids is Sunday, May 1. Use this information to answer the questions.

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1. What is the third date on which Sophia will need to water the orchids?

2. What is the fifth date on which Sophia will need to water the orchids?

3. What is the seventh date on which Sophia will need to water the orchids?

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1. What is the third date on which Sophia will need to water the orchids?• Set up a calendar using what we know to find

the date.• The first day Sophia waters the orchids is May 1.

Fill in the calendar with this information.

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Date May 1 May 2 May 3 May 4 May 5 May 6 May 7

Day of week

Sun. Mon. Tues. Wed. Thurs. Fri. Sat.

Instances of watering the orchids

First time

• The problem tells us that Sophia waters the orchids every three days. Three days from May 1 is Wednesday, May 4, so the second time Sophia waters is May 4. Three days after May 4 is May 7.

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Day of week



First time

Second time

Third time

• The third time Sophia waters the orchids is May 7. How can we use this information to find the fifth and seventh dates? What connection can we make between the third instance of watering and the date being May 7?

• From the calendar, we see that at each instance of watering, the date has increased by 3 days. The first watering day is on May 1, the second is on May 4, and the third is on May 7. So we can say the number associated with the date should be 3 times the number associated with the instance of watering, or 3n, where n is the nth time Sophia needs to water the orchids.

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• Check the formula by substituting values for n. Use 1, 2, and 3 for the first, second, and third times Sophia waters the orchids.

3n = x3(1) = 3 = May 33(2) = 6 = May 63(3) = 9 = May 9

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• These dates don’t match what we see on the calendar. We need to adjust our formula so that the first watering is on May 1.

• If we subtract 2 from 3n, we get the following:3n – 2 = x3(1) – 2 = 1 = May 13(2) – 2 = 4 = May 43(3) – 2 = 7 = May 7

• The formula 3n – 2 = x, where n is the nth watering and x is the date, is correct for the first, second, and third times Sophia needs to water the orchids.

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2. What is the fifth date on which Sophia will need to water the orchids?• Substitute 5 into the formula 3n – 2 = x.

3n – 2 = x3(5) – 2 = 15 – 2 = 13

• The fifth time Sophia needs to water the orchids is on May 13. Check this using the calendar.

• We need to expand our calendar table for another week.

• Add a week to the calendar and fill it out to check what we’ve found.

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• The formula predicted correctly the fifth watering day on May 13.

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Day of week



First time

Second time

Third time

Date May 8 May 9 May 10

May 11 May 12

May 13

May 14

Day of week



Fourth time

Fifth time

3. What is the seventh date on which Sophia will need to water the orchids?• Substitute 7 into the formula 3n – 2 = x.

3n – 2 = x3(7) – 2 = 21 – 2 = 19

• The formula predicts that Sophia will water the plants on May 19. Add another week to the calendar and confirm.

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Day of week



First time

Second time

Third time

Date May 8 May 9 May 10

May 11 May 12

May 13

May 14

Day of week



Fourth time

Fifth time

• We see the formula 3n – 2 = x is able to predict the watering dates for Sophia.

• The third, fifth, and seventh dates on which Sophia must water the orchids are May 7, May 13, and May 19.

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Date May 15

May 16 May 17

May 18

May 19

May 20

May 21

Day of week



Sixth time

Seventh time

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