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# What is the sum of the multiples of 7 from 84 to 140, inclus

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Re: What is the sum of the multiples of 7 from 84 to 140, inclus  [#permalink]

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20 Jun 2017, 18:57
LM wrote:
What is the sum of the multiples of 7 from 84 to 140, inclusive?

A. 896
B. 963
C. 1008
D, 1792
E. 2016

We can use the following equation to determine the quantity:

(largest multiple in the set - smallest multiple in the set)/7 + 1 = number of multiples of 7

(140 - 84)/7 + 1

56/7 + 1 = 9

Next, let’s determine the average of this evenly spaced set.

average = (first number + last number)/2

average = (84 + 140)/2 = 224/2 = 112

Thus, the sum is 9 x 112 = 1,008.

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Re: What is the sum of the multiples of 7 from 84 to 140, inclus  [#permalink]

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01 Sep 2018, 10:26
$$140-84=56$$
$$\frac{56}{7}$$ + 1 = 9
so there are 9 multiples of 7 between 84 and 140. so now apply sum formula.
$$S=\frac{n}{2}(2a+(n-1)d)$$
where S is sum, n is total number of terms, a is first number in series and d is distance between numbers in series.
so n=9, d=7, a=84
$$S=1008$$
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Hasnain Afzal

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Re: What is the sum of the multiples of 7 from 84 to 140, inclus  [#permalink]

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01 Sep 2018, 10:42
Use the concept of Ap....Check if the last digit is divisible by 7 or not. If divisible then that will be last term...Now find nth term....You will get number of terms...Use the formula of sum of terns where first term is 84 and last term is 140 and number of terms is 9. Check the basic concepts of Arithmetic Progression.

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Re: What is the sum of the multiples of 7 from 84 to 140, inclus   [#permalink] 01 Sep 2018, 10:42

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