## anonymous 5 years ago does anyone know what the general terms of this sequence is 3,6,10,15

1. anonymous

yes

2. anonymous

lol can you help me

3. anonymous

sorry i didnt got you

4. anonymous

it is a arithmetic sequence with a twist.

5. anonymous

so how do i do it

6. anonymous

how does each sequence differs

7. anonymous

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

8. anonymous

yes

9. anonymous

now what do i do

10. anonymous

do you know the form for an arithmetic sequence?

11. anonymous

no

12. anonymous

ok ill give you the form for that and then you can try to relate it to this problem. $\sum_{n=1}^{N}n=N*(N+1)/2$

13. anonymous

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

14. anonymous

what does n represent

15. anonymous

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

16. anonymous

can you these formulas for series?

17. anonymous

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.

18. anonymous

do we alway use this formula for finding the general term

19. anonymous

no not always

20. anonymous

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

21. anonymous

for the series

22. anonymous

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

23. anonymous

24. anonymous

lets break the terms into sums 1+2 1+2+3 1+2+3+4 ... so if n denotes the term we have $\sum_{i=1}^{n+1}i=(n+1)*(n+2)/2=(n^{2}+3n+2)/2$

25. anonymous

so n=1: (1+3+2)/2=3 you can check the other terms if you want

26. anonymous

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

27. anonymous

this is the simplest way I know to do it.

28. anonymous

okay ty

29. anonymous

yep, hope it helped a bit :)

30. anonymous

yah it did ty