Question 54. Find the sum of all even integers between 101 and 999.

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Asked: June 30, 20212021-06-30T22:24:27+05:30 2021-06-30T22:24:27+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 even integers between 101 and 999 by using the arithmetic properties sum formula

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Class:- 10th
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Question 54

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AAREKH · Answer 1 · 2021-07-01T10:20:44+05:30

All even integers between 101 and 999 are 102, 104, 106, 108, . . . . 998.

First term(a) = 102, common difference(d) = 104 – 102 = 2 and nth term(a_n) = 998.

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

a_n = a + (n – 1)d

So,

=> 998 = 102 + (n – 1)2

=> 2(n – 1) = 896

=> n – 1 = 448

=> n = 449

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

S_n = n[a + a_n] / 2

So,

S₄₄₉ = 449[102 + 998] / 2

= 449[550]

= 246950