Question

Im so lost on this problem, I dont know where to start.... Any help would be great.

Each sequence or series involves four quantities, for example, a1, an, d, r, n, and Sn.
describe the four quantities and Then explain how you can find the fourth quantity if you know the values of the other three.

A) an=a1 + (n-1) d

B) sn= n/2 ( a1-an)

C) an=a1r ^ n-1

D) Sn = a1 ( 1-r^n) / 1-r

Answer 1

if the serie is artihmetic then you have to use A and B
A helps you to find a term of the serie for example if you want to find the 5th term you should write 5 instead of n
B helps you to find the sum of the serie until the term you choose. If you find the sum until 3rd term (a1+a2+a3) you have to write 3 instead of n.
C and D is nearly same but you have to use these formulations with geometric series. C is like A and D is like B.

Answer 2

but it still doesnt make sense to me, how do i do it? Thank ypu for helping

Answer 3

a1 means the first term
an means the general term
d means common difference between two terms at arithmetic series for example let your serie be like
2 4 6 8 10
then your d=2
r means common factor between your two terms at geometirc series for ex. let your seris be like
2 4 8 16 32
then your r=2

Answer 4

Sn means sum
for example s2=a1+a2
s4=a1+...+a4

Answer 5

I know that, but do i just plug the equations into each other? how you can find the fourth quantity if you know the values of the other three?

Answer 6

lets define a serie
2 5 8 and ?
you look at difference between two terms it is 3
so the difference between 3rd and 4th term must be 3
add 3 to 8 it is 11
so a4=11
you can generalize it like that
the difference is 3 so you have to start your general term with 3n
and first term is 2 so when you put 1 to 3n it must be 2 so you have to organise it like that an=3n-1
lets try it
we found that a4=11 put 4 in our equation 3n-1 it is 11 as u can see

Answer 7

Ok....I know what a series is, but the problem is asking "Each sequence or series involves four quantities, for example, a1, an, d, r, n, and Sn.
describe the four quantities and Then explain how you can find the fourth quantity if you know the values of the other three" Thats the part i dont get and im having trouble with

Answer 8

i did in my last description and explained how to find the fourth quanitity if u know the values of the other three. sorry but i didnt understand your question

Answer 9

Its ok, Thank you. So i use B to find a sum, What will that do? What can i use it for, I think thats what i need help with

Answer 10

n is the term quantity if you want to find the sum of first 4 term (a1+a2+a3+a4) you write 4 into n
and write the a1 and a4 into their place.
but your equation must be n/2*(a1+an) so you find it from there

Answer 11

So would this work?
an = a1+nd-d
an-nd = a1-d
n(a-d) = a1-d
n = (a1-d)/(a-d)
4=(a1-d)/(a-d)

Answer 12

i will say you easier way to find sum

Answer 13

sum= (middle term)*(number of terms)
=(last term+first term)/2*(number of terms)
=(an+a1)/2*(n)

Answer 14

this is feasible at every arithmetic sequence

Answer 15

I still just dont get it....What does that do, Is my way right?

Answer 16

you need to read these...
http://www.regentsprep.org/Regents/math/algtrig/ATP2/ArithSeq.htm

http://www.regentsprep.org/Regents/math/algtrig/ATP2/GeoSeq.htm

Answer 17

I dont think you guys understand, I know what a series and sequence is. The part im stuck on is what to do with them... With the equations, what can i do??? Thats the part i dont get