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Write the multiples of 4 between 10 and 30.

Answer
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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)10822
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)302827
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,
a1=a=12
a2=a+d=12+4=16
a3=a+2d=12+2×4=20
a4=a+3d=12+3×4=24
a5=a+4d=12+4×4=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.
4×1=4
4×2=8
4×3=12
4×4=16
4×5=20
4×6=24
4×7=28
4×8=32
4×9=36
And so on.
So, the numbers between 10 and 30 which are multiples of 4 are 12, 16, 20, 24 and 28.
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