Arithmetic
What is the explicit formula for arithmetic sequences?
an = a1 + (n-1)(d)
Three times one number added to six times another number is 9. Four times the first number plus 5 times the second number is 15. What are the two numbers?
The numbers are -1 and 5.
What does the nth term of a sequence mean?
The position in the pattern you are looking for.
What is the explicit formula for geometric sequences?
an = (a1)(r n-1)
What type of sequence does this situation represent AND what rule?
-5, 2, 9, 16, …
Arithmetic d=+7
A water tank develops a leak. The tank is losing 10 gallons of water each week. The tank when full contained 1000 gallons of water. Write an explicit formula representing the situation. How many gallons of water is in the tank after 12 weeks.
910 gl
Determine whether the sequence is arithmetic, geometric or neither. Justify your reasoning.
3. 1, 2, 4, 7, …
Neither
What type of sequence does this situation represent AND what rule?
1, 4, 16, 64, …
Geometric r=x4
Generate the first 5 terms of a sequence using the recursive formula.
an=an-1 -3 , a1=7
a2=7 - 3 = 4
a3=4 - 3 = 1
a4=1 - 3 = -2
a5=-2 - 3 = -5
You need to earn at least $300 per week working as a manager of a restaurant and teaching guitar lessons. You earn $15 per hour at the restaurant and $30 per hour teaching lessons. You not want to work more than 20 hours total.
X=Hours at restaurant y=Hours as teacher
15x + 30y > 300
x + y <20
There should be lines under the symbol but I can't do that in this program.
Turn y=2x+4 into an explicit formula!
an = 4 + (n - 1)(2)
Generate the first 5 terms of a sequence using the geometric recursive formula.
an=(an-1)(2) , a1=-3
a2=-3 - 3 = -6
a3=-6 - 3 = -9
a4=-9 - 3 = -12
a5=-12 - 3 = -15
Write an equation for the nth term of each sequence, and find the indicated term.
21, 19, 17, … find a50
-77
Tracy wants to start saving money gradually. She decided to save $5 the first month, $10 the second month, $15 the third month, and so on. If she continues this savings plan, how much money will she save during the 11th month?
a11= 55.
What is the 13th term in this pattern? Or how many plus signs will there be?
+
++
+++
13
Barbara shares a photo with five of her friends. Each of her friends shared the photo with five more friends, and so on. How many people received the photo after the 8th round?
320 People.
The first four terms of an arithmetic sequence are 28, 20, 12, and 4. Which term of the sequence is -36?
It is the 9th term.
You need at least 6 pounds of fruit for a desert recipe. Blueberries cost $4 a pound and strawberries cost $3 a pound. You have at most $24 to spend. Write a system of inequalities for this situation.
X=lb of Blueberries y=lb of Blueberries
4x + 3y < 24
x + y >6
There should be lines under the symbol but I can't do that in this program.
What is Mr. Beasley's favorite color?!
GREEN
Find the eighth term of a geometric sequence for which a3=81 and r = 3.
19,683