English

Find the Sum of All Natural Numbers Between 200 and 400 Which Are Divisible by 7. - Mathematics

Advertisements
Advertisements

Question

Find the sum of all natural numbers between 200 and 400 which are divisible by 7.

Advertisements

Solution

Natural numbers between 200 and 400 which are divisible by 7 are 203, 210 ,.... 399.
This is an AP with a = 203, d = 7 and l = 399.
Suppose there are n terms in the AP. Then,

an = 399 

⇒ 203 + (n-1) × 7 = 399                   [an = a+ (n-1) d] 

⇒ 7n + 196 =399

⇒ 7n = 399-196 =203

⇒ n = 29 

`∴  "Required sum " = 29/2 (203+399)               [ s_n = n/2 (a+l)]`

`= 29/2 xx 602`

= 8729

Hence, the required sum is 8729.

shaalaa.com
  Is there an error in this question or solution?
Chapter 11: Arithmetic Progression - Exercises 4

APPEARS IN

R.S. Aggarwal Mathematics [English] Class 10
Chapter 11 Arithmetic Progression
Exercises 4 | Q 13

RELATED QUESTIONS

Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120


In an AP: Given a = 5, d = 3, an = 50, find n and Sn.


In an A.P., the sum of first n terms is `(3n^2)/2 + 13/2 n`. Find its 25th term.


If numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n and its next two terms.


The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?


How many numbers are there between 101 and 999, which are divisible by both 2 and 5?


If `4/5 `, a, 2 are in AP, find the value of a.


If the sum of first n terms is  (3n+  5n), find its common difference.


Find the sum of all even numbers between 1 and 350.

The A.P. in which 4th term is –15 and 9th term is –30. Find the sum of the first 10 numbers.


Sum of 1 to n natural numbers is 36, then find the value of n.


Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....

 

Q.7


Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.


Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.


If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are ______.


The sum of all odd integers between 2 and 100 divisible by 3 is ______.


If the last term of an A.P. of 30 terms is 119 and the 8th term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.


In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25th term of the A.P.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×