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# Question 52. Find the sum of all integers between 84 and 719, which are multiples of 5.

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One of the most important and exam oriented question from Chapter name- Arithmetic Progression
Class 10th
Chapter number- 9
Exercise :- 9.6
This type of question has been asked in previous years exams.
In this question we have been asked to find the sum of all integers between 84 and 719, which are multiples of 5.

CBSE DHANPAT RAI publication
CBSE Mathematics Class 10th
Question 52

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1. Integers between 84 and 719, which are multiples of 5 are 85, 90, 95, 100, . . . . 715.

First term(a) = 85, common difference(d) = 90 – 85 = 5 and nth term(an) = 715.

By using the formula of nth term of an A.P.

an = a + (n – 1)d

So,

=> 715 = 85 + (n – 1)5

=> 5(n – 1) = 630

=> n – 1 = 126

=> n = 127

Now by using the formula of sum of n terms of an A.P.

Sn = n[a + an] / 2

So,

S127 = 127[85 + 715] / 2

= 127

= 50800

Hence, the sum of all integers between 84 and 719, which are multiples of 5 is 50800.

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