Mackiemesseridn
Answered

Get personalized answers to your unique questions on IDNLearn.com. Our platform provides detailed and accurate responses from experts, helping you navigate any topic with confidence.

What will be the next digit in the sentence 1, 1, 2, 3, 5, 8, 13, 21, 34?
Please show me your way of thinking :)

Sagot :

Riya25idn
It's Fibonacci :

so you have 
1, 1, 2, 3, 5, 8, 13, 21, 34, 55

Basically, to find out the number:

13=5+8
21=13+8
34=21+13
55=34+21

The next number is the sum of the previous two.
[tex]This\ is\ a\ Fibonacci\ sequence:\\1;\ 1;\ 2;\ 3;\ 5;\ 8;\ 13;\ 21;\ 34;...\\\\a_1=1\\a_2=1\\a_3=a_1+a_2=1+1=2\\a_4=a_2+a_3=1+2=3\\a_5=a_3+a_4=2+3=5\\a_6=a_4+a_5=3+5=8\\a_7=a_5+a_6=5+8=13\\a_8=a_6+a_7=8+13=21\\a_9=a_7+a_8=13+21=34\\a_{10}=a_8+a_9=21+34=55\\a_{11}=a_9+a_{10}=34+55=89\\a_{12}=a_{10}+a_{11}=55+89=144\\\vdots[/tex]


[tex]a_n=a_{n-2}+a_{n-1}[/tex]-The next number is the sum of the previous two.
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com has the solutions you’re looking for. Thanks for visiting, and see you next time for more reliable information.