Advertisements
Advertisements
Question
What is the sum of an odd numbers between 1 to 50?
Advertisements
Solution
The odd numbers between 1 to 50 are
1, 3, 5, ......, 49
The above sequence is an A.P.
∴ a = 1
∴ d = 5 – 3 = 2
Let the number of terms in the A.P. be n.
Then, tn = 49
Since tn = a + (n – 1)d,
49 = 1 + (n – 1)(2)
∴ 49 = 1 + 2n – 2
∴ 49 = 2n – 1
∴ 49 + 1 = 2n
∴ n =`50/2`
∴ n = 25
Now, `S_n = n/2 (t_1 + t_n)`
∴ `S_25 = 25/2 (1 + 49)`
= 12.5 × 50
= 625
∴ The sum of odd numbers between 1 to 50 is 625.
APPEARS IN
RELATED QUESTIONS
Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term of the A.P.
The first and last terms of an AP are 17 and 350, respectively. If the common difference is 9, how many terms are there, and what is their sum?
Find the sum of first n odd natural numbers
The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. Find the AP.
HINT: Let these terms be (a – d), a, (a + d).
Find the sum of the first n natural numbers.
Divide 207 in three parts, such that all parts are in A.P. and product of two smaller parts will be 4623.
The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.
In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 − S10)
Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.
If `4/5` , a, 2 are three consecutive terms of an A.P., then find the value of a.
The number of terms of the A.P. 3, 7, 11, 15, ... to be taken so that the sum is 406 is
Let the four terms of the AP be a − 3d, a − d, a + d and a + 3d. find A.P.
Q.17
Find the sum of odd natural numbers from 1 to 101.
Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years.
Find the next 4 terms of the sequence `1/6, 1/4, 1/3`. Also find Sn.
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?
