How many multiples of 4 lie between 10 and 250? ​

Question

How many multiples of 4 lie between 10 and 250?

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Valentina 2 months 2021-12-03T09:25:50+00:00 2 Answers 0 views 0

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    0
    2021-12-03T09:26:51+00:00

    \bf{\underline{Solution}}:-

    Multiples of 4 lie between 10 and 250 are 12,16,20………..,248.

    This is an Arithmetic progression (AP)

    Given :-

    • First term (a) = 12
    • Common difference (d) = 16-12 = 4
    • \rm\:a_n=248

    To find :-

    • How many multiples of 4 lies between 10 and 250

    Solution :-

    We know that,

    \blue{\bigstar}\:\:{\underline{\boxed{\bf\red{a_n=a+(n-1)d}}}}

    248 = 12 + (n – 1) × 4

    248 – 12 = (n – 1) × 4

    236 = (n – 1) × 4

    \rm\dfrac{236}{4}=n-1

    59 = n – 1

    59 + 1 = n

    60 = n

    n = 60

    Hence,60 multiples of 4 lies between 10 and 250.

    More Information :

    Sequence : some numbers arranged in a definite order, according to a definite rule,are said to form a sequence.

    • The number occuring at the nth place of sequence is called nth term which is denoted by Tn or an.

    0
    2021-12-03T09:27:42+00:00

    How many multiples of 4 lie between 10 and 250?

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    Hey,

    The answer is 60.

    Method 1: To arrive at the answer, we can either list down all the multiples of 4 between 10 and 250 and count them. This however is a little time consuming. So, lets move onto the other alternatives.

    Method 2: First let us find the number of multiples of 4 between 1 and 10 which would be 10/4=2.5

    Number of multiples of 4 between 1 and 250 = 250/4=62.5

    So, the number of multiples of 4 between 10 and 250 would be

    (Number of multiples of 4 between 1 and 250) – (Number of multiples of 4 between 1 and 10)

    62.5−2.5=60

    Method 3: We need to find the number of multiples of 4 between 10 and 250.

    The list of numbers would be as follows:

    12,16,20,24,28,32,36,40,……..248.

    The above list is an arithmetic series/arithmetic progression where the first number is 12, the last number is 248 and the common difference between the numbers is 4.

    The nth term in an arithmetic sequence = a + (n-1)*d where a is the first term, d is the common difference.

    In the arithmetic series above, a =12, d = 4 and let us assume there are n terms and we need to find the value of n. We know that the value of the last term i.e. nth term is 248.

    So, 248=12+(n−1)∗4

    248=12+4n−4

    248=4n+8

    248–8=4n

    240=4n

    n=240/4=60

    Thus, 248 is the 60th term in the series and hence there are 60 terms in the series.

    Therefore number of multiples of 4 between 10 and 250 is 60.

    Hope this helps.

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