Question

when do you use the formula a_n = a_1+ (n-1)d

Answer 1

When you want to find the nth term (or a specific term) of an arithmetic sequence.

Answer 2

what about S_n= n/2 (a_1+a_n)

Answer 3

also can i have an exaple for each i wanna make sure i got this :)

Answer 4

When you want to find the nth partial sum from the first term to the nth term

Answer 5

Oh and this partial sum is of an arithmetic sequence

Answer 6

ok what about S_n=(2a_1+(n-1)d)

Answer 7

Example:

If a_1 = 3 and d = 5 then


a_n = a_1+ (n-1)d

a_n = 3+ (n-1)5

a_n = 3+5n-5

a_n = 5n-2


So the nth term is 5n-2


The 6th term is then

a_6 = 5(6)-2

a_6 = 28

Answer 8

okay :)

Answer 9

That last equation looks like a sequence, but why did you use S_n?

Answer 10

thats what my paper says, it says tell when i would use each formula and that one has a S_n in frunt

Answer 11

hmm I'm not familiar with that form, one sec

Answer 12

ok

Answer 13

I'm thinking there's a typo since S_n implies it's a partial sum but the right side implies it's a sequence.

Answer 14

ok then il have to tell my teacher about that one but what about a_n = a_1r^(n-1)

Answer 15

that represents the nth term of a geometric sequence

Answer 16

S_n=(a_1-a_1r^n)/1-r

Answer 17

and that's the nth partial sum of a geometric sequence from the first term a_1 to the nth term a_n

Answer 18

and last one S_n=(a_1-a_nr)/1-r

Answer 19

hmm looks similar to the last equation, but it's not equivalent

Answer 20

and I'm not finding anything similar to what you wrote

Answer 21

um ok thanks for trying tho you helped me lots

Answer 22

alright, glad I did