Question

What are the next 3 numbers in this pattern of integers -2, -1, -1, 0, -1, 1, -2

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Answer 1

The next 3 numbers to the given pattern of integers is -2,-1,-1,0,-1,1,-2 are 3,-5,8

Explanation:

Given pattern of integers is -2,-1,-1,0,-1,1,-2

To find their next 3 numbers of the given pattern :

Let
`a_(1)=-2`

`a_(2)=-1`

`a_(3)=a_(1)-a_(2)`

`=-2-(-1)`

`=-2+1`

Therefore
`a_(3)=-1`

`a_(4)=a_(2)-a_(3)`

`=-1-(-1)`

`=-1+1`

Therefore
`a_(4)=0`

Similarly we have
`a_(5)=-1` ,
`a_(6)=1` ,
`a_(7)=-2`

The general form to the given pattern is

`a_(n)=a_(n-2)+a_(n-1)` for
`n={\{1,2,3,4,5,6,7,8,9,10}\}`

Therefore to find the
`a_(8),a_(9),a_(10)`

Put n=8 in
`a_(n)=a_(n-2)-a_(n-1)`

`a_(8)=a_(8-2)-a_(8-1)`

`=a_(6)-a_(7)`

`=1-(-2)`

`a_(8)=3`

Put n=9 in
`a_(n)=a_(n-2)-a_(n-1)`

`a_(9)=a_(9-2)-a_(9-1)`

`=a_(7)-a_(8)`

`=-2-(3)`

`a_(9)=-5`

Put n=10 in
`a_(n)=a_(n-2)-a_(n-1)`

`a_(10)=a_(10-2)-a_(10-1)`

`=a_(8)-a_(9)`

`=3-(-5)`

`a_(10)=8`

Therefore the next 3 numbers are 3,-5,8