Advertisements
Advertisements
प्रश्न
The sum of first n natural numbers is given by `1/2n^2 + 1/2n`. Find the sum of natural numbers from 11 to 30.
Advertisements
उत्तर
Given, sum of first n natural numbers = `1/2n^2 + 1/2n`
Sum of natural numbers from 11 to 30
= Sum of first 30 natural numbers – Sum of first 10 natural numbers
= `[1/2(30)^2 + 1/2(30)] - [1/2(10)^2 + 1/2(10)]`
= `900/2 + 30/2 - 100/2 - 10/2` ...[Divide each term by 2]
= 450 + 15 – 50 – 5
= 410
APPEARS IN
संबंधित प्रश्न
Write down the following in the product form: x2y4
Write down the following in the product form: 10a3b3c3
If 9 is added to a certain number, the result is 36. Find the number.
If 11 is subtracted from 4 times a number, the result is 89. Find the number.
The sum of three consecutive natural numbers is 114. Find the numbers.
The sum of three consecutive odd numbers is 21. Find the numbers.
Reena is 6 years older than her brother Ajay. If the sum of their ages is 28 years, what are their present ages?
The perimeter of the triangle shown in the following figure is ______.
The area of a square having each side x is ______.
The two digit number whose ten’s digit is ‘t’ and units’s digit is ‘u’ is ______.
If I spend f rupees from 100 rupees, the money left with me is ______ rupees.
The side of an equilateral triangle is shown by l. Express the perimeter of the equilateral triangle using l.
To find sum of three numbers 14, 27 and 13, we can have two ways:
- We may first add 14 and 27 to get 41 and then add 13 to it to get the total sum 54 or
- We may add 27 and 13 to get 40 and then add 14 to get the sum 54. Thus, (14 + 27) + 13 = 14 + (27 + 13)
This can be done for any three numbers. This property is known as the associativity of addition of numbers. Express this property which we have already studied in the chapter on whole numbers, in a general way, by using variables a, b and c.
Find the perimeter of the figure given below:
In a rectangular plot, 5 square flower beds of side (x + 2) metres each have been laid (see the figure). Find the total cost of fencing the flower beds at the cost of ₹ 50 per 100 metres:
The sum of first n natural numbers is given by `1/2n^2 + 1/2n`. Find the sum of first 11 natural numbers.
The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of table of 7.
If 
= 2x + 3, 
= `3/2x + 7` and 
= x – 3 then find the value of:
`1/2`
+ 
– 3
