Question

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

Answer 1

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