body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

6. Arithemetic Sequences

Finish the assignment

Continue to next subchapter

Exercise 45 Page 205

Practice makes perfect

a

To write a function representing an arithmetic sequence with the first term a_1 and common difference 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+5n-5

Subtract term

f(n)=5n

The function f(n)=5n represents the arithmetic sequence.

b

Let's identify the ordered pairs (n,a_n) we need to graph.

Minutes after January 1st	1	2	3	4
Total babies born	5	10	15	20
Ordered pairs	(1,5)	(2,10)	(3,15)	(4,20)

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)=5n

f(n)= 100

100=5n

.LHS /5.=.RHS /5.

20=n

Rearrange equation

n=20

From midnight on January 1st, it takes 20 minutes for 100 babies to be born.

Subchapter links

Communicate Your Answer p.199

Monitoring Progress p.200-203

Exercises p.204-206