Recursive Formula
Is the sequence...
2,4,6,8,10,12,14
Arithmetic or Geometric?
Arithmetic.
It adds 2 each time from the previous term.
Tom had 131 dollars to spend on 6 books. After buying them, he had 17 dollars left. How much did each book cost.
Each book cost 19 dollars
Determine the number of solutions of.....
x2 + 14x + 49
One
Complete the square and find the x values:
x2+ 14x = -24
x = -2 and x = -12
Factor the equation,
x3 + 9x2 + 23x + 15; x + 5
(x+5)(x2 + 4x + 3)
Or
(x + 5)(x + 1)(x + 3)
What is an example of a Geometric sequence, with the first term being 2 and it multiplies by 3 each time?
(Use a calculator if needed!)
2,6,18,54,162
A large cake is in a room. The first person who comes in takes 1/3 of the cake. The second person takes 1/3 of what is left. Then a third person takes 1/3 of what is left. And so on.
Create a table to complete a recursive sequence.
Hint: Start with 0 and think of what you have in total!
1 , 2/3 , 4/9 , 8/27 , 16/81
Determine the number of solutions of.....
x2 - 7x - 36
Two
Complete the square and find the x values:
x2 - 4x = 32
x = 8 and x = -4
Rewrite each polynomial as a product of linear factors:
f(x) = x3 - x2 - 14x + 24; x - 3
(x - 3)(x2 + 2x - 8)
Or
(x - 3)(x + 4)(x - 2)
What;s the difference between Arithmetic and Geometric sequence's?
Arithmetic; adding a certain number to the previous term.
Geometric; Multiplying a certain number to the previous one.
One art studio has an initial member fee of $20. They charge $100 per month to be a member.
A different art studio has an initial fee of $60, but charges $80 per month.
After how many months will the second art studio be cheaper.
After 2 months the second studio will be cheaper.
x4 - 14x3 - 6x2 + 59x + 6
Four
Complete the square and find the x values:
(x + 3)(x - 5) =
x2 - 2x - 15
Rewrite each polynomial as a product of linear factors:
f(x) = 3x3 - 4x2 - 9x + 10; x - 2
(x - 2)(3x2 + 2x - 5)
Write a recursive formula for...
2, 7, 12, 17
f(1) = 2, f(n) = 5 + f(n-1), n ≥ 2
The difference of squares of two consecutive even integers is 68. What are these integers?
Use the equation:
(x+2)2 - (x)2 = 68
x=16
The integers are 16 and 18
Determine the number of solutions of.....
x4 + 3x3
Two
Complete the square and find the x values:
(x + 3)2 = 25
x = 2 and x = -8
Rewrite each polynomial as a product of linear factors (Extra 100 points if you can do both box method and give me all the factors)
f(x) = x3 - 7x2 + 2x + 40; x - 5
(x - 5)(x2 - 2x - 8)
Or
(x - 5)(x - 4)(x + 2)
Write an nth term formula for...
2, 7, 12, 17
f(n) = 2 + 5( n - 1), n ≥1
Priya wants to sketch a graph of the polynomial f defined by f(x) = x3 + 5x2 + 2x - 8. She knows f(1) = 0, so she suspects that (x - 1) could be a factor of x3 + 5x2 + 2x -8 and writes (x3 + 5x2 + 2x - 8) = (x - 1) times what?
Factor it to find it, (Use divistion of polynomials or the boxes to help)
(x - 1)(x 2- 6x + 8)
Or
(x - 2)(x - 4)(x - 1)
Determine the number of solutions of.....
x3 + 2x2 + 15x - 1
One
y = x2 + 10x - 9
y = ( x + 5)2 - 34
Factor the equation;
6x3 + 7x2 - 1; 2x + 1
(2x + 1)(3x2 + 2x - 1)
Or
(3x - 1)(x + 1)(2x + 1)