Adi X.

asked • 04/20/17

This a question from 'numbers' section of maths.

If T1=1, T2= 2, & Tn= Tn-1+Tn-2  for all n>2, find the remainder when T21 is divided by 6 ??

2 Answers By Expert Tutors

By:

David W. answered • 04/20/17

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4.7 (90)

Experienced Prof

Adi X.

Sir this approach seems fine till I am asked T21 but what if something like T1000 or such terms are asked, then finding that term will obviously not be possible, then what to do???
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04/21/17

David W.

The remainders repeat for every 24 terms [proof left to student]:
 
1   2   3   5   2   1   3   4   1   5  
0   5   5   4   3   1   4   5   3   2  
5   1   0   1
 
Thus, the remainder of ( T21 / 6 ) is 5.
 
( 1000 / 6 )  is 41 Remainder 16
The 16th remainder in the list is 1, so the remainder of ( T1000 / 6) is 1.
 
Here are the remainders of T1 to T1000:
 
1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2
5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1
4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5
5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4
1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5

2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1
1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2
5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1
4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5
5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4

1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5
2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1
1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2
5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1
4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5

5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4
1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5
2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1
1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2
5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1

4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5
5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4
1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5
2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1
1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2

5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1
4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5
5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4
1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5
2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1

1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2
5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1
4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5
5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4
1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5

2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1
1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2
5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1
4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5
5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4

1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5
2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1
1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2
5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1
4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5

5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5 2 1 3 4
1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1 1 2 3 5
2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2 5 1 0 1
1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1 4 5 3 2
5 1 0 1 1 2 3 5 2 1 3 4 1 5 0 5 5 4 3 1
 
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04/21/17

David W.

The remainders repeat every 24 [note: proof left to sdudent1:
1 2 3 5 2 1 3 4 1 5
0 5 5 4 3 1 4 5 3 2
5 1 0 1
 
The 21st remainder in the list is 5.  The remainder of ( T21 / 6 ) is 5.

The 1000th remainder in the list is 1.  The remainder of ( T1000 / 6 ) is 1.
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04/21/17

David W.

The remainders repeat every 24 [note: proof left to sdudent1:
1 2 3 5 2 1 3 4 1 5
0 5 5 4 3 1 4 5 3 2
5 1 0 1

The 21st remainder in the list is 5.  The remainder of ( T21 / 6 ) is 5.

The 1000th remainder in the list is 1.  The remainder of ( T1000 / 6 ) is 1.
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04/21/17

Katie B.

I truly appreciate your answer for Adi's sake, but your statement about being a certified WyzAnt e-tutor was hostile. We're all approved for certain subjects, and I know there are areas I'm more knowledgeable than you in, but I'm not rubbing your nose in it.
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04/21/17

David W.

To Katie B.,
 
I've asked WyzAnt -- the Answers Forum is intended to match students to potential tutors.  Thus, there are multiple answers for questions and students are permitted to ask any number of questions (WyzAnt says that they monitor this).
 
The Answers Forum is deliberately limited.  Months ago, I reported a problem that makes me edit my Answers using HTML.  Sometimes, comments do not appear until many minutes later (as in this case, I responded in comments, then modified the answer).
 
Some WyzAnt tutors have been certified by WyzAnt for tutoring on-line (and they encourage this in the job searching capability).  The interactive white board allows graphics, voice/video. displaying documents and video, etc., etc.  I mentioned that I can do this for a potential e-tutor situation.
 
Best wishes on finding students to tutor.  It is rather clear from a simple query of students on the WyzAnt site that there are lots of needy students and there certainly are diverse tutors.
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04/22/17

Katie B.

I'm also capable of providing online sessions, and I'm very familiar with the platform. Good luck to you.
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04/23/17

Katie B. answered • 04/20/17

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5.0 (91)

Patient and knowledgeable Chemistry, Math, Science, English tutor

Adi X.

Mam,I think u mistook it, T4= T3+T2=5 not 6 & the series will be like 
1,2,2+1=3, 3+2=5,8,13..... So T4= 5.
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04/21/17

Katie B.

My apologies 
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04/21/17

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