Question

Write the multiples of 4 between 10 and 30.

Answer 1

Hint: We have to look for multiples of 4 that lie between 10 and 30. The multiples of 4 are the numbers that successfully increase by a difference of 4. So the multiple of 4 makes an AP with the common difference (d) as 4. Then we will divide 10 by 4 to get the nearest number divisible by 4 and greater than 10 which will give us the first term (a) of the AP and then we will divide 30 by 4 to get the last term. Once, we have the first term (a) and the difference (d), we will find the multiples of 4.

Complete step-by-step answer:
We are asked to find the multiples of 4 that lie between 10 and 30. We know that the multiples of 4 mean the number which is divisible by 4. The gap between the successive multiple is always 4. So, we get that the multiples of 4 will make an arithmetic progression with the common difference of 4, i.e. d = 4.
We do not know about the first term. We are asked to find the number greater than 10 which is a multiple of 4.
Now, to find the first term, we will divide 10 by 4.
\[4\overset{2}{\overline{\left){\begin{align}
  & 10 \\
 & \underline{8} \\
 & 2 \\
\end{align}}\right.}}\]
10 divided by 4 gives us the remainder 2. But multiple of 4 are perfectly divisible, so we add (Divisor – Remainder) to the dividend to make a perfect multiple. Now, 4 – 2 = 2.
So, we get 2 to 10, so that we get a number perfectly divisible by 4. We get a number 10 + 2 = 12
Therefore, our first term is 12, i.e. a = 12.
Now, we are given to look up to 30, so again we divide 30 by 4.
\[4\overset{7}{\overline{\left){\begin{align}
  & 30 \\
 & \underline{28} \\
 & 2 \\
\end{align}}\right.}}\]
30 divided by gives us the remainder 2, as we cannot cross 30, so we will subtract the remainder from the dividend to get the perfect multiple, i.e. 30 – 2 = 28.
So, our last term is 28.
So, we have to start at 12 and go up to 28.
So, we get the terms as,
\[{{a}_{1}}=a=12\]
\[{{a}_{2}}=a+d=12+4=16\]
\[{{a}_{3}}=a+2d=12+2\times 4=20\]
\[{{a}_{4}}=a+3d=12+3\times 4=24\]
\[{{a}_{5}}=a+4d=12+4\times 4=28\]
So, the multiples of 4 which lie between 10 and 30 are 12, 16, 20, 24 and 28.

Note: We can use an alternate method to find the solution. We can try a hit and try the method. We can start writing all the multiples of 4 and then pick the number that lies between 10 and 30.
The multiples of 4 are as follows.
\[4\times 1=4\]
\[4\times 2=8\]
\[4\times 3=12\]
\[4\times 4=16\]
\[4\times 5=20\]
\[4\times 6=24\]
\[4\times 7=28\]
\[4\times 8=32\]
\[4\times 9=36\]
And so on.
So, the numbers between 10 and 30 which are multiples of 4 are 12, 16, 20, 24 and 28.