Advertisements
Advertisements
प्रश्न
Find the sum of first n even natural numbers.
Advertisements
उत्तर
The first n even natural numbers are 2, 4, 6, 8, 10, …., n.
Here, a = 2 and d =(4-2)= 2
Sum of n terms of an AP is given by
`s_n = n/2 [ 2a + (n-1) d]`
`= (n/2) xx [ 2xx2+ (n-1) xx 2 ] `
`=(n/2) xx [ 4 + 2n -2 ] = (n/2 ) xx (2n +2 ) = n(n+1)`
Hence, the required sum is n(n+1).
APPEARS IN
संबंधित प्रश्न
Find the sum given below:
–5 + (–8) + (–11) + ... + (–230)
Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,
Find the sum of first 51 terms of an A.P. whose 2nd and 3rd terms are 14 and 18 respectively.
Find the middle term of the AP 10, 7, 4, ……., (-62).
How many two-digit number are divisible by 6?
A sum of ₹2800 is to be used to award four prizes. If each prize after the first is ₹200 less than the preceding prize, find the value of each of the prizes
If k,(2k - 1) and (2k - 1) are the three successive terms of an AP, find the value of k.
There are 25 rows of seats in an auditorium. The first row is of 20 seats, the second of 22 seats, the third of 24 seats, and so on. How many chairs are there in the 21st row ?
What is the sum of first 10 terms of the A. P. 15,10,5,........?
If the seventh term of an A.P. is \[\frac{1}{9}\] and its ninth term is \[\frac{1}{7}\] , find its (63)rd term.
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?
Write the nth term of an A.P. the sum of whose n terms is Sn.
Write the sum of first n even natural numbers.
If S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2} =\]
Let the four terms of the AP be a − 3d, a − d, a + d and a + 3d. find A.P.
How many terms of the series 18 + 15 + 12 + ........ when added together will give 45?
The first term of an AP of consecutive integers is p2 + 1. The sum of 2p + 1 terms of this AP is ______.
The sum of first five multiples of 3 is ______.
Find the sum of all odd numbers between 351 and 373.
Solve the equation:
– 4 + (–1) + 2 + 5 + ... + x = 437
