» CC HOME » FORUM HOME

 College Confidential VERY HARD SEQUENCE Q's FOR CALCULUS AB/BC MATH BUFFS ONLY!!
 User Name Remember Me? Password New User

Welcome to College Confidential!
The leading college-bound community on the web
Join for FREE now, and start talking with other members, weighing in on community polls, and more.

Also, by registering and logging in you'll see fewer ads and pesky welcome messages (like this one)!
 Discussion Menu »Discussion Home »Help & Rules »Latest Posts »NEW! CampusVibe™ »Stats Profiles Top Forums »College Chances »College Search »College Admissions »Financial Aid »SAT/ACT »Parents »Colleges »Ivy League Main CC Site »College Confidential »College Search »College Admissions »Paying for College Sponsors SuperMatch - The Future of College Search! CampusVibe - Almost As Good As A Campus Visit!
 04-05-2006, 05:20 PM #1 Member   Join Date: Jun 2005 Location: Washington, D.C. and Newark, NJ Posts: 787 VERY HARD SEQUENCE Q's FOR CALCULUS AB/BC MATH BUFFS ONLY!! Hey. The following are questions that I got from an old worksheet on sequences, but I can't find the answers.... I thought that I would post them here to give you guys some practice, but also since I want to see if I am correct. REMEMBER: THESE QUESTIONS ARE EXTREMELY HARD, BUT SHOULD MATCH THE DIFFICULTY OF THOSE ON THE EXAM. Find the next number and GENERAL TERM for each of the following sequence. Justify each answer. 1) 3,8,15,24,35,48... 2) 6,14,18,28,30,42... 3) 1/6, 1/3, 1/2, 2/3, 5/6, 1,... 4) 4,1,0,1,4,9... 5) 2,8,26,80,242,728... 6) 15,210,63,220,243,230... 7) 2,7,4,14,6,21... 8) -1,4,1,6,3,8 9) 1,5,13,29,61,125... 10) 10,21,33,46,60,75... Thanks guys. Good luck! (I doubt any of you guys can figure out the answers anyway ). Reply
 04-05-2006, 05:30 PM #2 Senior Member   Join Date: Aug 2004 Location: New York City Posts: 3,962 is 10) 91? Reply
 04-05-2006, 05:31 PM #3 Senior Member   Join Date: Aug 2004 Location: New York City Posts: 3,962 is 9) 253? Reply
 04-05-2006, 05:48 PM #4 Member   Join Date: Jun 2005 Location: Washington, D.C. and Newark, NJ Posts: 787 I need the general formula... thanks! Reply
 04-05-2006, 06:07 PM #5 Member   Join Date: Nov 2005 Posts: 608 3,8,15,24,35,48. 5 7 9 11 13 15 2 2 2 2 2 so 15+48 = 63. This can be done for all of them to find the next term. As far as the pattern, um no clue. This was on the WPI programming contest and I didnt have a clue. 4) 4,1,0,1,4,9... (n-1)^2 assuming that n starts at 1 and its 16 2) 6,14,18,28,30,42... for the odds its 6n, and for the even its 7n the seventh term is 6*7 = 42. 7) 2,7,4,14,6,21... odd = 2n even = 7n 8) -1,4,1,6,3,8 odd = n-2 even = 2n 3) 1/6, 1/3, 1/2, 2/3, 5/6, 1,... it goes 1*6 * n(n-1) but I cant make this a formula. Last edited by mattd1688; 04-05-2006 at 06:23 PM. Reply
 04-05-2006, 07:33 PM #6 Junior Member   Join Date: Dec 2005 Posts: 142 #10 10n+(n-1)(n)/2 Solution: first notice that its a sequence of 0 1 3 6 10... plus 10n. well, 0 1 3 6 10... is known as triangle number and its explicit formula is (n-1)n/2. i don't know how to derive this explicit formula, but that's what it is and i memorized it. Thus, the answer is 10n+(n-1)(n)/2 Reply
 04-05-2006, 07:37 PM #7 Junior Member   Join Date: Dec 2005 Posts: 142 #3 is arithmetic. it's just n/6 Reply
 04-05-2006, 07:55 PM #8 Member   Join Date: Feb 2006 Posts: 481 These are ridiculously easy and by no means need calculus to solve. If you want I can post solutions... just tell me the numbers you want. I dunno about the AP Calculus test, but you will probably NOT encounter these types of problems... if there was an AP Algebra2 test then you definitely would. Reply
 04-05-2006, 08:06 PM #9 Member   Join Date: Jun 2005 Location: Washington, D.C. and Newark, NJ Posts: 787 Surge... what are the answers for #1-10 then... (big shot).. haha. Thanks Reply
 04-05-2006, 08:07 PM #10 Member   Join Date: Jun 2005 Location: Washington, D.C. and Newark, NJ Posts: 787 Answers to seq. questions Could you post the forumlas for #1-10, if they are "so-easy."" I would really appriciate it. Thanks Reply
 04-05-2006, 08:12 PM #11 Member   Join Date: Feb 2006 Posts: 481 Sorry, if I came off as a "big shot"... lemme just finish my spanish homework and I'll post 'em. Reply
 04-05-2006, 08:41 PM #12 Member   Join Date: Jun 2005 Location: Washington, D.C. and Newark, NJ Posts: 787 Thank you surge... I really appriciate it! Reply
 04-05-2006, 08:42 PM #13 Member   Join Date: Feb 2006 Location: Pittsburgh Posts: 667 mattd's answers - i think he assumed the first value is for n = 1, I would change the n's to (n+1)(all my edits are going off his technique) #4 doesn't seem to work..... at n=1 in that, the answer would be 0. #2 looks good #7 - almost right. for odds its not 2n, its 1+ n #8 looks good stanfordream #10 doesn't work for me..... if you plug in 1 for n, the result isn't 1., its 10. surge #3 is exactly right. nice spot. mine (btw, this is assuming that the first value is at n = 0....... all of my analyses.) #1 look at pattern for odds 3 = 1 x 3 15 = 3 x 5 35 = 5 x 7 next number = 63 = 7 x 9 for evens, its 8 = 2 x 4 24 = 4 x 6 48 = 6 x 8 so general equation = (n+1)(n+3) #4 (n-2)^2 -next number is 16. #5 3 times the previous number + 2 (not sure how to write that in symbols)- next number = 2186 #6 odds- 3*3^(n-1)*(5+n) evens- 200 + 10n (for some reason, I can't get #6 to work out w/ the first value correlating to n = 0..... it has to be n= 1. #10 previous number + 10 + n -next number is 91 there. skipped 9 cause i couldn't do it quick. that should be all of them. Reply
 04-05-2006, 09:17 PM #14 Member   Join Date: Feb 2006 Posts: 481 All answers I believe have been posted except for 9. Number 9 is a special case... it cannot be solved using finite differences. Probably because it is an exponential equation. HINT: For all other problems Use finite differences. Set up coefficient matrices in your calculator for linear, quadratic, cubic and quartic. Take the inverse of your coefficient matrix (after you figure out what power its to by using finite differences) and multiply it by your solution matrix (which should nx1, where n is one higher than the degree of your polynomial and equal to the number of rows in your coefficient matrix). EDIT: woops, some people posted recursive formulas (regarding the last term). Lemme post some explicit formulas. Reply
 04-05-2006, 09:22 PM #15 Member   Join Date: Feb 2006 Posts: 481 #10 explicit= (1/2)x[x+19] Reply

 Bookmarks