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18 March, 09:19

Find the number of multiples of 7 between 30 and 300. Is it 38?

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  1. 18 March, 09:40
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    Yes it is 38 ...
  2. 18 March, 12:38
    0
    In the above problem, you want to find the number of multiples of 7 between 30 and 300.

    This is an Arithmetic progression where you have n number of terms between 30 and 300 that are multiples of 7. So it is evident that the common difference here is 7.

    Arithmetic progression is a sequence of numbers where each new number in the sequence is generated by adding a constant value (in the above case, it is 7) to the preceding number, called the common difference (d)

    In the above case, the first number after 30 that is a multiple of 7 is 35

    So first number (a) = 35

    The last number in the sequence less than 300 that is a multiple of 7 is 294

    So, last number (l) = 294

    Common difference (d) = 7

    The formula to find the number of terms in the sequence (n) is,

    n = ((l - a) : d) + 1 = ((294 - 35) : 7) + 1 = (259 : 7) + 1 = 37 + 1 = 38
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