Advertisements
Advertisements
प्रश्न
What is the sum of an odd numbers between 1 to 50?
Advertisements
उत्तर
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
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
Find the sum of the following APs:
`1/15, 1/12, 1/10`, ... to 11 terms.
In an AP, given a = 7, a13 = 35, find d and S13.
In an AP given a = 3, n = 8, Sn = 192, find d.
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Find the sum of the following arithmetic progressions:
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.
Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Which term of the A.P. `20, 19 1/4, 18 1/2, 17 3/4,` ... is the first negative term?
In an A.P. 17th term is 7 more than its 10th term. Find the common difference.
If the sum of n terms of an A.P. is Sn = 3n2 + 5n. Write its common difference.
The common difference of the A.P. \[\frac{1}{2b}, \frac{1 - 6b}{2b}, \frac{1 - 12b}{2b}, . . .\] is
Two cars start together in the same direction from the same place. The first car goes at uniform speed of 10 km h–1. The second car goes at a speed of 8 km h–1 in the first hour and thereafter increasing the speed by 0.5 km h–1 each succeeding hour. After how many hours will the two cars meet?
A sum of Rs. 700 is to be paid to give seven cash prizes to the students of a school for their overall academic performance. If the cost of each prize is Rs. 20 less than its preceding prize; find the value of each of the prizes.
A manufacturer of TV sets produces 600 units in the third year and 700 units in the 7th year. Assuming that the production increases uniformly by a fixed number every year, find:
- the production in the first year.
- the production in the 10th year.
- the total production in 7 years.
Q.1
Q.13
First four terms of the sequence an = 2n + 3 are ______.
In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25th term of the A.P.
Solve the equation:
– 4 + (–1) + 2 + 5 + ... + x = 437
