SequencesSection 14.1

SequencesSuppose that a town’s present population of 100,000 is growing by 5% each year.

After the first year, the town’s population will be:100,000 + 0.05(100,000) = 105,000

After the second year, the town’s population will be:105,000 + 0.05(105,000) = 110,250

After the third year, the town’s population will be:110,250 + 0.05(110,250) ≈ 115,763

SequencesIf we continue to calculate, the town’s yearly population can be written as the infinite sequence of numbers

105,000, 110,250, 115,763, ….

If we decide to stop calculating after a certain year (say, the fourth year), we obtain the finite sequence

105,000, 110,250, 115,763, 121,551

Sequences An infinite sequence is a function whose

domain is the set of natural numbers {1, 2, 3, 4, …}

Ex. 2, 4, 6, 8, …

A finite sequence is a function whose domain is the set of natural numbers {1, 2, 3, 4, …, n}, where n is some natural number.

Ex. 1, -2, 3, -4, 5

Writing the terms of a Sequence𝑎𝑛=2

𝑛

is known as the general term

Writing the terms of a Sequence

First term Second termThird term

Tenth term

Example 1:Write the first three terms of the sequence whose general term is given by .

Evaluate , where n is 1, 2, and 3.

Replace n with 1

Example 1:Write the first three terms of the sequence whose general term is given by .

Evaluate , where n is 1, 2, and 3.

Replace n with 2

Example 1:Write the first three terms of the sequence whose general term is given by .

Evaluate , where n is 1, 2, and 3.

Replace n with 3

OYO: Write the first four terms of the sequence whose

general term is given by .

Example 2:If the general term of a sequence is given by , find

a. the first term of the sequence

Example 2:If the general term of a sequence is given by , find

b.

Example 2:If the general term of a sequence is given by , find

c. the one-hundredth term of the sequence

Example 2:If the general term of a sequence is given by , find

d.

OYO: If the general term of a sequence is given by ,

finda. the first term of the sequence

b.

c. The thirtieth term of the sequence

d.

Example 3: Finding the general term of a sequenceFind a general term of the sequence whose first few terms are given. a. 1, 4, 9, 16, … Terms are all squares.

Example 3: Finding the general term of a sequenceFind a general term of the sequence whose first few terms are given. b. Terms are all reciprocals.

Example 3: Finding the general term of a sequenceFind a general term of the sequence whose first few terms are given. c.

Example 3: Finding the general term of a sequenceFind a general term of the sequence whose first few terms are given. d. Terms double each time.

OYO:Find a general term of the sequence whose first few terms are given. a. b. 3, 9, 27, 81, ...

Example 4: ApplicationThe amount of weight, in pounds, a puppy gains in each month of its first year is modeled by a sequence whose general term is , where n is the number of the month. Write the first five terms of the sequence, and find how much weight the puppy should gain in its fifth month.

The puppy should gain 9 pounds in its fifth month.

OYO:The value v, in dollars, of an office copier depreciates according to the sequence , where n is the time in years. Find the value of the copier after three years.

The copier would only be worth $2022.40 after three years.

HOMEWORK Unit 19 homework page (on the back of

your unit plan)

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