SOLUTION: You have a series of numbers, where the sum of the previous two numbers (except for the first two) adds up to the next one. (Like the Fibanachi sequence), the first number is 1 and

Algebra ->  Sequences-and-series -> SOLUTION: You have a series of numbers, where the sum of the previous two numbers (except for the first two) adds up to the next one. (Like the Fibanachi sequence), the first number is 1 and      Log On


   

Question 310517: You have a series of numbers, where the sum of the previous two numbers (except for the first two) adds up to the next one. (Like the Fibanachi sequence), the first number is 1 and the 10th number is 111. What is the second number?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Let the 2nd number be x.  Then the numbers are

#1.  1
#2.  x
#3.  1+x
#4.  x+(1+x)=x+1+x=1+2x
#5.  (1+x)+(1+2x)=1+x+1+2x=2+3x
#6.  (1+2x)+(2+3x)=1+2x+2+3x=3+5x
#7.  (2+3x)+(3+5x)=2+3x+3+5x=5+8x
#8.  (3+5x)+(5+8x)=3+5x+5+8x=8+13x
#9.  (5+8x)+(8+13x)=5+8x+8+13x=13+21x  
#10. (8+13x)+(13+21x)=8+13x+13+21x=21+34x

Since term #10 is 111:

21%2B34x=111
34x=90
x=90%2F34
x=45%2F17

Checking, the numbers go

1=17%2F17,45%2F17,62%2F17,107%2F17,169%2F17,276%2F17,445%2F17,721%2F17,1166%2F17,1887%2F17=111

Edwin