Question

What's the difference between geometric and arithmetic sequences?
How do you put them in summation notation?

Answer 1

what definitions do they give you?

Answer 2

We don't have any
I just don't know what they are in general

Answer 3

arithmetic is adding ... you are adding the same value one term to get to the next term

geometric is similar, but its multiplying the value instead of adding

Answer 4

a summation notation is simply taking the rule that defines the sequence, and adding all the terms that the sequence generates

Answer 5

for example:

lets add 3 to some seed value: 2

2
2+3 = 5
5+3 = 8
8+3 = 11
11+3 = 14
etc ....

Answer 6

so squence would be
2, 5, 8, 11, 14
a1, a2, a3, a4, a5

Answer 7

yes, sometimes its convenient to start at n=0, but thats not important :)

Answer 8

maybe i'll actually pass my math quiz

Answer 9

notice that we can make a rule for the sequence.

a1 = 2 + 3(0)
a2 = 2 + 3(1)
a3 = 2 + 3(2)
a4 = 2 + 3(3)
a5 = 2 + 3(4)

for every value of n, we add an (n-1) multiple to our seed value

Answer 10

so the rule that explicitly defines this sequence that we are generating is: 2 + 3(n-1)

Answer 11

lets apply this concept to a geometric sequence: a common ratio is the conventioanl term to use for the common value. lets call it 'r' with the same seed value of 2

g1 = 2r^0
g2 = 2r^1
g3 = 2r^2
g4 = 2r^3
g5 = 2r^4

in general, the explicit rule for this geometric sequence is: 2r^(n-1)

Answer 12

any questions?

Answer 13

I think I got it all
I guess we'll see how we do

Answer 14

goodluck ;)