Advertisements
Advertisements
प्रश्न
Write the sum of first n even natural numbers.
Advertisements
उत्तर
In this problem, we need to find the sum of first n even natural numbers.
So, we know that the first odd natural number is 2. Also, all the odd terms will form an A.P. with the common difference of 2.
So here,
First term (a) = 2
Common difference (d) = 2
So, let us take the number of terms as n
Now, as we know,
`S_n = n/2 [2a + (n-1)d]`
So, for n terms,
`S_n = n/2 [ 2(2) + (n-1) 2]`
`= n/2 [4 + 2n - 2 ]`
`= n/2 ( 2 + 2n)`
`= n(1 +n)`
Therefore, the sum of first n even natural numbers is `S
_n = n(n +1)` .
APPEARS IN
संबंधित प्रश्न
The ratio of the sum use of n terms of two A.P.’s is (7n + 1) : (4n + 27). Find the ratio of their mth terms
In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?
In an A.P., the sum of first n terms is `(3n^2)/2 + 13/2 n`. Find its 25th term.
The sum of n natural numbers is 5n2 + 4n. Find its 8th term.
The 8th term of an AP is zero. Prove that its 38th term is triple its 18th term.
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.
The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.
The sum of first n terms of an A.P is 5n2 + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P.
Ramkali would need ₹1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved ₹50 in the first month of this year and increased her monthly saving by ₹20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?
The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.
In an A.P. sum of three consecutive terms is 27 and their products is 504. Find the terms. (Assume that three consecutive terms in an A.P. are a – d, a, a + d.)
The sum of all odd integers between 2 and 100 divisible by 3 is ______.
Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.
[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]
Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.
If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.
Find the sum of all odd numbers between 351 and 373.
Find the middle term of the AP. 95, 86, 77, ........, – 247.
Find the sum of all even numbers from 1 to 250.
Three numbers in A.P. have the sum of 30. What is its middle term?
