Yahoo! Group Title Find the n th term and sum of n terms of the series 5 + 8 + 17 + 44 .......... one year ago one year ago

1. dpflan Group Title

Ah, this is a nice series. $[5,8,17,44]$

2. experimentX Group Title

find the difference .. note the difference in the difference is a multiple of 3

3. Yahoo! Group Title

Yes the first order difference is in Gp

4. dpflan Group Title

and on...so do as @experimentX suggests, first examine any sort of relationship that could exist, you see that each termer is greater than the next

5. dpflan Group Title

I suggest that you show us the values you have for the difference between the numbers in the series

6. dpflan Group Title

Once, you have those differences, see if there is a pattern or relationship among them

7. zepp Group Title

Looks like 3 to some power :D

8. experimentX Group Title

tn+1 = tn + 3^(n-1)

9. dpflan Group Title

term1 = 5 term2 = 8 term2 - term1 = 3 so term2 = term1 + 3 term3 = 17 term3 - term2 = 9 so term3 = term2 + 9 term4 = 44 term5 - term4 = 27 so term4 = term3 + 27 term5 = ...

10. experimentX Group Title

don't know closed form at the moment!!

11. dpflan Group Title

So @Yahoo! How are you doing with this?

12. Yahoo! Group Title

Ar^n + b1n^k-1 + b2n^k-2............bk

13. dpflan Group Title

Hmm, can you explain the terms please?

14. Yahoo! Group Title

it is the general formula lol1

15. sami-21 Group Title

ok look at the sequence first term is (3^1+7)/2=5 second is (3^2+7)/2=8 third is (3^3+8)/2=17 can you now tell me general formula ?

16. experimentX Group Title

i guess we should use summation rule |dw:1343147827410:dw|

17. mahmit2012 Group Title

|dw:1343147906405:dw|

18. mahmit2012 Group Title

|dw:1343147929358:dw|

19. experimentX Group Title

not sure that works!

20. experimentX Group Title

|dw:1343147968035:dw| something like that!! just try to manipulate and fit in it ...

21. mahmit2012 Group Title

|dw:1343147962155:dw|

22. experimentX Group Title

|dw:1343148038487:dw|

23. mahmit2012 Group Title

|dw:1343148023475:dw|

24. amistre64 Group Title

i like to get the first term to 1 alot of times 5 + 8 + 17 + 44 -4 -4 -4 -4 ----------------- 1 + 4 + 13 + 40 just helps me with the inbetween addings or if we up it by +1 5 + 8 + 17 + 44 +1 +1 +1 +1 ------------------- 6 + 9 + 18 + 45

25. amistre64 Group Title

factor out a 3 3( 2 + 3 + 6 + 15 + ...) all ways to se it differently

26. experimentX Group Title

|dw:1343148174027:dw|

27. experimentX Group Title

i hope it works for other terms too .. let's see for sum

28. Yahoo! Group Title

@experimentX i didnt understand!!

29. experimentX Group Title

|dw:1343148311125:dw|

30. experimentX Group Title

that's just some manipulation .. typing in latex really takes lot of time

31. experimentX Group Title

$t_n = t_{n-1} + 3^{n-1}$ this is the general rule $t_{n} = t_{n-2} + 3^{n -2} + 3^{n-1}$ continue this way and you will get $t_{n} = t_1 + 3 + 3^3 + 3^4+ .. + 3^{n -2} + 3^{n-1} = 5 + 3{ 3^{n-1} - 1 \over 3-1}$ which is requited formula

32. experimentX Group Title

for summation $\sum_{n=1}^k {5 + {3 \over 2} (3^{n - 1 } - 1)} =\sum_{n=1}^k{7/2} + 3^n = k {7 \over 2}+ 3{3^k -1 \over 3-1} = k {7 \over 2}+ {3 \over 2}(3^k -1)$ @Yahoo! do you understand??

33. mahmit2012 Group Title

|dw:1343149457407:dw|

34. mahmit2012 Group Title

@experimentX I guess you missed 1/2 .

35. experimentX Group Title

thanks @mahmit2012 for correction ... you are sharp!!ii

36. Yahoo! Group Title

@mahmit2012 @experimentX i learnt this by using this Ar^n + b1n^k-1 + b2n^k-2............bk

37. Yahoo! Group Title

formula!1

38. mahmit2012 Group Title

You're welcome , and good tutoring you have had. @experimentX

39. Yahoo! Group Title

Ar^n + b1n^k-1 + b2n^k-2............bk

40. Yahoo! Group Title

can u ssolve this by using Ar^n + b1n^k-1 + b2n^k-2............bk

41. experimentX Group Title

you are a good tutor!! most of me is autodidact!!