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
How many terms of the AP. 9, 17, 25 … must be taken to give a sum of 636?
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 ×(5 + 3)]
The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceed the second term by 6, find three terms.
Find the sum of the following arithmetic progressions:
`(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y)`, .....to n terms
Find the sum 2 + 4 + 6 ... + 200
Find the sum of the first 15 terms of each of the following sequences having the nth term as
yn = 9 − 5n
The 9th term of an AP is -32 and the sum of its 11th and 13th terms is -94. Find the common difference of the AP.
If (3y – 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value of y.
Find four numbers in AP whose sum is 8 and the sum of whose squares is 216.
Find the sum of all natural numbers between 200 and 400 which are divisible by 7.
Write an A.P. whose first term is a and common difference is d in the following.
a = –3, d = 0
In an A.P. the 10th term is 46 sum of the 5th and 7th term is 52. Find the A.P.
The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is
If the first term of an A.P. is a and nth term is b, then its common difference is
In a Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find that:
(i) first term
(ii) common difference
(iii) sum of the first 20 terms.
The sum of all odd integers between 2 and 100 divisible by 3 is ______.
If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25th term of the A.P.
The 5th term and the 9th term of an Arithmetic Progression are 4 and – 12 respectively.
Find:
- the first term
- common difference
- sum of 16 terms of the AP.
