Exercise 45 Page 205

Practice makes perfect

a To write a function representing an arithmetic sequence with the first term

a_{1}

d,

we can use the following equation.

f (n) = a_{1} + (n - 1) d

From the table we can see that the first term is

5 .

We can also see that the difference between each pair of consecutive terms (the common difference) is

5 .

Let's substitute these values into the equation.

f (n) = a_{1} + (n - 1) d

$a_{1} = 5$ , $d = 5$

f (n) = 5 + (n - 1) 5

Distribute $5$

f (n) = 5 + 5 n - 5

Subtract term

f (n) = 5 n

The function

f (n) = 5 n

represents the arithmetic sequence.

b From the table let's identify the ordered pairs

(n, a_{n})

we need to graph.

Let's plot them on a coordinate plane.

c We will use the function from Part A to find the value of

n

when

f (n) = 100 .

f (n) = 5 n

$f (n) = 100$

100 = 5 n

$LHS / 5 = RHS / 5$

20 = n

Rearrange equation

n = 20

From midnight on January

1 st

it takes

20

minutes for

100

babies to be born.

Communicate Your Answer p.199

Monitoring Progress p.200-203

Exercises p.204-206

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