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pychu [463]
3 years ago
8

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

Mathematics
1 answer:
sashaice [31]3 years ago
4 0

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 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

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