Question

Study the following number patterns:

$45\times 9+2=407$

$456\times 9+3=4107$

$4567\times 9+4=41107$

Find the next 2 lines.
[4 MARKS]

Answer 1

Application: 2 Marks
Steps: 1 Mark
Answer: 1 Mark

This pattern is like this:-

$45\times 9+2=407$

$456\times 9+3=4107$

$4567\times 9+4=41107$

For next three lines, it would be like this-
As we can see in the pattern, the number of digits is incremented by 1, and the units digit is the successor of the previous number.
Also, the number which we are adding to the product is incremented by 1.
Using distributive property we can make the calculations simpler for the following,

$45678\times 9+5=45678\times (10-1)+5$
$=456780-45678+5=411107$

$456789\times 9+6=456789\times (10-1)+6$
$=4567890-456789+6=4111107$