Question

Write the next three numbers in the following and explain the rule that is followed by the numbers:

$24, 19, 14,_____,_____,_____$

Accepted Answer

The rule that is followed by these numbers is an arithmetic progression, where each subsequent number is obtained by subtracting a constant value to the previous number. In this case, the constant value is $24, 19, 14,_____,_____,_____$ .

Start with the first number, which is $24$ .

To find the second number, subtract $5$ from the first number: $24 - 5 = 19$

To find the third number, subtract $5$ from the second number: $19 - 5 = 14$

So, each number in the sequence is found by taking the previous number and subtracting $5$ from it. This creates an arithmetic progression with a common difference of $- 5$ .

Now, to find the next three numbers:

To find the fourth number, subtract $5$ from the third number: $14 - 5 = 9$

To find the fifth number, subtract $5$ from the fourth number: $9 - 5 = 4$

To find the sixth number, subtract $5$ from the fifth number: $4 - 5 = - 1$

Therefore, the next three numbers in the sequence are $9, 4$ and $- 1$ .

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