Advertisements
Advertisements
Question
Find the sum of first n odd natural numbers
Advertisements
Solution
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)`
`= n^2`
Therefore, the sum of first n odd natural numbers is `S_n = n^2`
RELATED QUESTIONS
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
Find the sum of the following APs.
`1/15, 1/12, 1/10`, ......, to 11 terms.
If the 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
Find the sum of all even integers between 101 and 999.
The sum of three consecutive terms of an AP is 21 and the sum of the squares of these terms is 165. Find these terms
If k,(2k - 1) and (2k - 1) are the three successive terms of an AP, find the value of k.
Find the 25th term of the AP \[- 5, \frac{- 5}{2}, 0, \frac{5}{2}, . . .\]
If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)
Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .
Here a = 1 , d =b`[ ], t_n = 149`
tn = a + (n-1) d
∴ 149 =`[ ] ∴149 = 2n - [ ]`
∴ n =`[ ]`
The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
If 18, a, b, −3 are in A.P., the a + b =
If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is
Q.19
In an AP if a = 1, an = 20 and Sn = 399, then n is ______.
The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?
In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021-22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year. |
Based on the above information answer the following questions.
- Find the production in the 1st year
- Find the production in the 12th year.
- Find the total production in first 10 years.
[OR]
In how many years will the total production reach 31200 cars?
If the first term of an A.P. is p, second term is q and last term is r, then show that sum of all terms is `(q + r - 2p) xx ((p + r))/(2(q - p))`.
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
The sum of A.P. 4, 7, 10, 13, ........ upto 20 terms is ______.
The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
