Pre calc unit 11

Question 1

In pascals triangle what are the first five rows
and how are the rows numbered

Answer 1

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

the rows go
0
1
2
3
4
5

Question 2

what equation would you use to solve
6th row 3rd element

Answer 2

n!/r!(n-r)!
n is the row and r is the element

Question 3

How would you solve (2k+1)^10
find the 6th element

Answer 3

10!/5!(10-5)!

Question 4

what is the geometric sequence explicit formula

Answer 4

gn = g1(r^n-1)

Question 5

What is the geometric recursive formula

Answer 5

g1 = ____
gn = g(down subscript: n-1)r
when n greater then or equal to 2

Question 6

what formula do you use to find the sum of an arthimetic series

Answer 6

sn = n(a1+an)/2

Question 7

what do the different things mean on a sigma(weird rectangle)
a. number on top
b. number on bottom
c. numbers to the right

Answer 7

a. the number on top is the term number so if its five that means you stop calculating when n = 5
b. the number on the bottom is the first number (number you start calculating with)
c. the big numbers to the right is the formula (what you plug the numbers in to

Question 8

what is the explicit arithmetic formula

Answer 8

an = a1 + d(n-1)

Question 9

what is the recursive arithmetic formula

Answer 9

a1 = ______
an = a(down subscript n-1) + d
when n is greater then or equal to 2

Question 10

what is a common difference formula
ex. a1 = 11 and a25 = 107 find d

Answer 10

d = (am-an)/(m-n)
ex. d = (107-11) /( 25-1)

Question 11

what is the formula for a geometric sum

Answer 11

sn = g1(1-r^n)/(1-r)

Question 12

a. how do you know if a series is convergent or divergent?
b. how do you find the sum of convergent series
c. when do you find if a series is convergent or divergent

Answer 12

a. if |r|<1 the series is convergent
if |r|>1 the series is divergent
b. a1/1-r
c. if a geometric series is infinite