Answer:
The next 3 numbers to the given pattern of integers is -2,-1,-1,0,-1,1,-2 are 3,-5,8
Step-by-step explanation:
Given pattern of integers is -2,-1,-1,0,-1,1,-2
To find their next 3 numbers of the given pattern :
Let [tex]a_{1}=-2[/tex]
[tex]a_{2}=-1[/tex]
[tex]a_{3}=a_{1}-a_{2}[/tex]
[tex]=-2-(-1)[/tex]
[tex]=-2+1[/tex]
Therefore [tex]a_{3}=-1[/tex]
[tex]a_{4}=a_{2}-a_{3}[/tex]
[tex]=-1-(-1)[/tex]
[tex]=-1+1[/tex]
Therefore [tex]a_{4}=0[/tex]
Similarly we have [tex]a_{5}=-1[/tex] ,[tex]a_{6}=1[/tex] ,[tex]a_{7}=-2[/tex]
The general form to the given pattern is
[tex]a_{n}=a_{n-2}+a_{n-1}[/tex] for [tex]n={\{1,2,3,4,5,6,7,8,9,10}\}[/tex]
Therefore to find the [tex]a_{8},a_{9},a_{10}[/tex]
Put n=8 in [tex]a_{n}=a_{n-2}-a_{n-1}[/tex]
[tex]a_{8}=a_{8-2}-a_{8-1}[/tex]
[tex]=a_{6}-a_{7}[/tex]
[tex]=1-(-2)[/tex]
[tex]a_{8}=3[/tex]
Put n=9 in [tex]a_{n}=a_{n-2}-a_{n-1}[/tex]
[tex]a_{9}=a_{9-2}-a_{9-1}[/tex]
[tex]=a_{7}-a_{8}[/tex]
[tex]=-2-(3)[/tex]
[tex]a_{9}=-5[/tex]
Put n=10 in [tex]a_{n}=a_{n-2}-a_{n-1}[/tex]
[tex]a_{10}=a_{10-2}-a_{10-1}[/tex]
[tex]=a_{8}-a_{9}[/tex]
[tex]=3-(-5)[/tex]
[tex]a_{10}=8[/tex]
Therefore the next 3 numbers are 3,-5,8
