Question

does anyone know what the general terms of this sequence is 3,6,10,15

Answer 1

yes

Answer 2

lol can you help me

Answer 3

sorry i didnt got you

Answer 4

it is a arithmetic sequence with a twist.

Answer 5

so how do i do it

Answer 6

how does each sequence differs

Answer 7

it increase by one each time so ,2,3,4,5

Answer 8

yes

Answer 9

now what do i do

Answer 10

do you know the form for an arithmetic sequence?

Answer 11

no

Answer 12

ok ill give you the form for that and then you can try to relate it to this problem.

\[\sum_{n=1}^{N}n=N*(N+1)/2\]

Answer 13

let me know if that's enough to get you started

Answer 14

what does n represent

Answer 15

n is just an integer. in the sum if you have N=3 you get 1+2+3=6= (3*4/2)

Answer 16

can you these formulas for series?

Answer 17

yes it will help you find a general form for this series in terms of n where n represents with term in the series you are at.

Answer 18

do we alway use this formula for finding the general term

Answer 19

no not always

Answer 20

are you looking for the series(sum) or sequence?

Answer 21

for the series

Answer 22

i just want a quick way of figuring out the general term

Answer 23

instead of keep guessing

Answer 24

lets break the terms into sums

1+2
1+2+3
1+2+3+4
...
so if n denotes the term we have

\[\sum_{i=1}^{n+1}i=(n+1)*(n+2)/2=(n^{2}+3n+2)/2\]

Answer 25

so n=1: (1+3+2)/2=3

you can check the other terms if you want

Answer 26

is there a a better way of figuring this out so you can avoid fractions in the general term

Answer 27

this is the simplest way I know to do it.

Answer 28

okay ty

Answer 29

yep, hope it helped a bit :)

Answer 30

yah it did ty