Question 55. Find the sum of all integers(iii) between 1 and 500 which are multiples of 2 as well as of 5.

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deepaksoniGuru

Asked: June 30, 20212021-06-30T22:36:08+05:30 2021-06-30T22:36:08+05:30In: CBSE

This is the basic and conceptual question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise 9.6

In this question we have been asked to find the sum of all integers between 1 and 500 which are multiples of 2 as well as of 5

CBSE DHANPAT RAI publications
Class:- 10th
Solutions of CBSE Mathematics
Question 55(iii)

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AAREKH · Answer 1 · 2021-07-01T10:17:07+05:30

AAREKH Guru

All integers between 1 and 500 which are multiples of 2 as well as of 5 are 10, 20, 30, 40, . . . .490.

First term(a) = 10, common difference(d) = 20 – 10 = 10 and nth term(a_n) = 490.

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

a_n = a + (n – 1)d

So,

=> 490 = 10 + (n – 1)10

=> 10(n – 1) = 480

=> n – 1 = 48

=> n = 49

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

S_n = n[a + a_n] / 2

So,

S₄₉ = 49[10 + 490] / 2

= 49[250]

= 12250