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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.

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.