Advertisements
Advertisements
Question
The sum of first n odd natural numbers is ______.
Options
2n - 1
2n + 1
n2
n2 - 1
Advertisements
Solution
The sum of first n odd natural numbers is n2.
Explanation:-
In this problem, we need to find the sum of first n odd natural numbers.
So, we know that the first odd natural number is 1. Also, all the odd terms will form an A.P. with the common difference of 2.
So here,
First term (a) = 1
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(1) + ( n- 1) 2 ]`
`=n/2[2+2n-2]`
`=n/2(2n)`
= n2
Therefore, the sum of first n odd natural numbers is `S_n = n^2`.
APPEARS IN
RELATED QUESTIONS
The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
Divide 32 into four parts which are in A.P. such that the product of extremes is to the product of means is 7 : 15.
If the term of m terms of an A.P. is the same as the sum of its n terms, show that the sum of its (m + n) terms is zero
Find the sum of all integers between 50 and 500, which are divisible by 7.
Is -150 a term of the AP 11, 8, 5, 2, ……?
The 4th term of an AP is 11. The sum of the 5th and 7th terms of this AP is 34. Find its common difference
Determine k so that (3k -2), (4k – 6) and (k +2) are three consecutive terms of an AP.
If an denotes the nth term of the AP 2, 7, 12, 17, … find the value of (a30 - a20 ).
Find the sum of the first n natural numbers.
The first term of an AP is p and its common difference is q. Find its 10th term.
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
The sum of first 9 terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1 : 2. Find the first and 15th term of the A.P.
There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.
How many terms of the A.P. 27, 24, 21, …, should be taken so that their sum is zero?
In an A.P. (with usual notations) : given a = 8, an = 62, Sn = 210, find n and d
What is the sum of an odd numbers between 1 to 50?
In a ‘Mahila Bachat Gat’, Sharvari invested ₹ 2 on first day, ₹ 4 on second day and ₹ 6 on third day. If she saves like this, then what would be her total savings in the month of February 2010?
Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77.
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
