1. Find the 5th and 6th no. in this sequence.
2. How many no.s are there in this sequence?
3. If this sequence continues,what is the number immediately after 2584/4181?
2007-08-09 21:24:44 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
1/2, 3/5, 8/13, 21/34,.... 55/ 89, 144/ 233
(2) I think the numbers could go on forever - head to infinity.
(3) 6765 / 10,946
How, this is how to work it out:
Take the first fraction and add the two numbers together (1 + 2) and you get 3. This is the top number on the next fraction. Now add the 3 to the bottom number of the previous fraction (3 + 2) and you get 5, which is the bottom number on the next fraction.
Now repeat the process.
2007-08-09 21:35:16 · answer #1 · answered by Sparks 6 · 0⤊ 0⤋
There is a famous sequence of numbers called the Fibonacci Sequence. Each number is the sum of the previous two numbers. It is:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc.
The sequence is unending. Your sequence is based on this. It takes the numbers by twos starting with the second number and forms them into fractions.
1) The fifth and sixth numbers in your sequence are:
55/89 and 144/233
________________
2) Since the sequence is unending, there are an infinite number of numbers in the sequence.
_________________
3) Using the rule to extend the sequence we have:
2584, 4181, 6765, 10946
Converting to your form the next number is:
6765/10946
2007-08-09 21:51:28 · answer #2 · answered by Northstar 7 · 1⤊ 0⤋
1/2,3/5,8/13,21/34, a/b
1+2 =3
2+3=5
3+5=8
5+8=13
8+13=21
13+21=34
21+34=55
34+55=89 so 5th term = 55/89
55+89 = 144
89+144=233 so 6th term = 144/233
2. this sequence has no limit, continues indefinitely
3. the number after 2584/4181 is 2584+4181 = 6765
2007-08-09 21:45:52 · answer #3 · answered by vlee1225 6 · 0⤊ 0⤋
1) numerator of the fraction is the sum of the digits of the previous fraction.
denominator is the sum of the numerator of the same fraction and the denominator of the previous one.
ie 1+2=3
3+2=5
5th number is (34+21)/(34+21+34)=55/89
similarly 6th no. is 144/233
2)infinite
3)6765/10946
2007-08-09 21:44:05 · answer #4 · answered by MathStudent 3 · 0⤊ 0⤋
1. 5th term : 55/34
6th term : 89/123
2. Infinite
3. Immediate term = 6765/9349
2007-08-09 22:08:38 · answer #5 · answered by anand t 2 · 0⤊ 0⤋
1/2 (1+2=3/5(3+2))
the numerator is
1\2 numerator of next is 3
3+2 denominator hence is 5
fifth no shall be 65/
bore ho gaya yaar hope u get the picture
2007-08-09 21:42:55 · answer #6 · answered by arpit m 2 · 0⤊ 1⤋
Q1: 55....Q2: infinite...Q3: 6765.. the Fibonacci sequence!
2007-08-09 21:37:13 · answer #7 · answered by andrea m 1 · 0⤊ 0⤋