Question

Study the pattern:
\[1\times 8+1=9\]
\[12\times 8+2=98\]
\[123\times 8+3=987\]
\[1234\times 8+4=9876\]
\[12345\times 8+5=98765\]
Write the next four steps. Can you find out how the pattern works?

Answer 1

Hint: We are given a question with a given pattern. Based on the given pattern, we have to write the next four steps of the given pattern. We will first find the terms which are iterating in every step. We can see that the unit digit of the number which is multiplied to 8 is the number added to it. This pattern is being followed in every step. Based on this rule, we will write the next four steps of the given pattern.

Complete step by step solution:
According to the given question, we are given a pattern. Based on the rule applied in the given pattern we are asked to write four more steps of the same pattern.
If we look closely and observe the first and the second line of the given pattern, we have,
\[1\times 8+1=9\] and \[12\times 8+2=98\]
We can see that the units place of the number which is multiplied to 8 is the number which is added to the product and so we get the respective answers.
The similar pattern is followed in the third, fourth and the fifth line as well. In the fifth line the number multiplied to 8 is 12345 so in the next step the number to be multiplied to 8 will be 123456.
So, the next four steps of the given pattern will be,
\[123456\times 8+6=987654\]
The next step is,
\[1234567\times 8+7=9876543\]
\[12345678\times 8+8=98765432\]
\[123456789\times 8+9=987654321\]
Therefore, we have the next four steps of the given pattern.

Note: The key to carry out more steps of the given pattern is to understand the rule applicable in each step. This is the most crucial step. If in place of the unit place, the tens place is written, the answer will get wrong.
There is another explanation to this pattern as well.
With the increasing number of steps, the number which is multiplied to 8 also increases, that is, at the fifth step the number multiplied to 8 is 12345 and the added number is also 5. Similarly, in the sixth step the number multiplied to 8 is 123456 and the number added to the product is 6. Hence, we can write more number steps in this way.