Question 5

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

Answer

The integers from 1 to 100, which are divisible by 2, are 2, 4, 6… 100.

This forms an A.P. with both the first term and common difference equal to 2.

⇒100 = 2 + (*n* –1) 2

⇒ *n* = 50

The integers from 1 to 100, which are divisible by 5, are 5, 10… 100.

This forms an A.P. with both the first term and common difference equal to 5.

∴100 = 5 + (*n* –1) 5

⇒ 5*n* = 100

⇒ *n* = 20

The integers, which are divisible by both 2 and 5, are 10, 20, … 100.

This also forms an A.P. with both the first term and common difference equal to 10.

∴100 = 10 + (*n* –1) (10)

⇒ 100 = 10*n*

⇒ *n* = 10

∴Required sum = 2550 + 1050 – 550 = 3050

Thus, the sum of the integers from 1 to 100, which are divisible by 2 or 5, is 3050.

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If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

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The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

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How many terms of G.P. 3, 3

^{2}, 3^{3}, … are needed to give the sum 120? - Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.

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(i) A = {x: x is an integer and - 3 < x < 7}.

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(iv) D = {x: x is a prime number which is divisor of 60}.

(v) E = The set of all letters in the word TRIGONOMETRY.

(vi) F = The set of all letters in the word BETTER. - Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

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Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

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Find the derivative of x at x = 1.

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Name the octants in which the following points lie:

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A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

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If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

- Q:-
Find the sum to

*n*terms of the series 5^{2}+ 6^{2}+ 7^{2}+ ... + 20^{2}

Priyanshu
2019-11-13 14:16:36

Thanks for the solution.

Shivanshu
2019-10-16 20:38:56

That is correct but I have asked other answer

Aarya
2019-09-16 17:47:16

Great..

Deekshitha
2019-09-16 05:44:54

Thanks sir it helped me

jitendra pushkar
2019-09-13 15:50:28

thanks sir.. ... wonderful answer.....

Subhash
2019-09-02 14:27:38

Thanks a lot

Ashutosh kumar
2019-08-26 16:05:50

Thanks sir

Asha
2019-08-23 16:04:41

Can it be solved by n(n+2)/2

Gunjan
2019-06-04 17:57:04

Thanks

Vivek singh
2019-05-18 21:14:49

Not best

- NCERT Chapter