bienes_joshua 2 years ago how many numbers between 25 and 400 are divisible by 11? what is their sum?

1. bienes_joshua

2. amistre64

well, it starts with the number 33

3. bienes_joshua

can u pls show the equation sir???

4. amistre64

400-25 = 375 possible results divide that by ll 375/11 = 34.1 so ill assume there is like 34 numbers in that

5. bienes_joshua

and the sum sir?

6. amistre64

there sum can be determined by the expression 33+11n from n=0 to 34 most likely

7. bienes_joshua

wait sir... 33+11n=????

8. sambhav__jain

9. amistre64

34 11 -- 34 34 ---- 374 11 ---- 385 11 ---- 396 .... found a few more

10. amistre64

pfft, for got to add 33 :) 374 +33 ---- 407 so it looks like 34 is too large and 33 is perfect 0 to 33

11. sambhav__jain

this time i am right i double checked it

12. bienes_joshua

can i ask for the solution sir??? because the solution is greatly needed

13. amistre64

33+11n i s a good expression yes since the first number divisible by 11 is 33

14. bienes_joshua

thanks sambhav

15. bienes_joshua

how to get the n sir???

16. amistre64

$\sum_{0}^{33}33+11n=\frac{33}{2}(33+374)$

17. sambhav__jain

a=33 l=396 d=11 n=(396-33/11)+1=35 sum=(35)(2(33)+34(11))/2 =7480 use the formula i gave u earlier

18. amistre64
19. bienes_joshua

thanks to to all of you friends :D

20. amistre64

the sum is 7293

21. bienes_joshua

why is sambhav answer is different?

22. amistre64

he most likely has a small error, or i do. but ive got the wolf to dbl chk me :) http://www.wolframalpha.com/input/?i=sum+%2833%2B11n%29%2C+n%3D0..33

23. sambhav__jain

hey @amistre64 ur formu;lla is correctbut ∑03333+11n=332(33+374) =6715.5

24. amistre64

yeah, 374 should have been 396 :) but i accounted for that afterwards

25. sambhav__jain

you used another website for help i used my mind

26. amistre64

at my age, the mind is not so good ;)

27. bienes_joshua

28. amistre64

i have to look at my left foot just to remember what color sock i need to put on the right foot :)

29. sambhav__jain

∑03333+11n=(35/2)(33+396)=7507.5

30. sambhav__jain

whats ur age @amistre64

31. amistre64

.... pretty old

32. bienes_joshua

sambhav and amistre what again is the answer???

33. amistre64

7293 is what i get

34. sambhav__jain

pls wait for a minute pls sorry for the argument between us

35. bienes_joshua

its just ok no hard feelings

36. amistre64

0 to 33 is 34 numbers entotal 34(33+396)/2 = 7293

37. bienes_joshua

its right tnx for all your help ive got 2 numbers to go can u cooperate me or help me sir???

38. amistre64

between the both of us, we are sure to work out all the wrinkles ;)

39. sambhav__jain

@bienes_joshua the write answer is 7293

40. bienes_joshua

much thanks of all your help i just need to finish the 2 problems i will close this question and write a new one :D

41. amistre64

starting an index at 1 makes life easier on the count but adds a little bit of complexity to the expression; therefore a modification that is equal is:$\sum_{1}^{34}33+11(n-1)$