Advertisements
Advertisements
प्रश्न
Find the sum of first 1000 positive integers.
Activity :- Let 1 + 2 + 3 + ........ + 1000
Using formula for the sum of first n terms of an A.P.,
Sn = `square`
S1000 = `square/2 (1 + 1000)`
= 500 × 1001
= `square`
Therefore, Sum of the first 1000 positive integer is `square`
उत्तर
Let 1 + 2 + 3 + ........ + 1000
Using formula for the sum of first n terms of an A.P.,
Sn = `"n"/2 ("t"_1 + "t"_"n")`
S1000 = `1000/2 (1 + 1000)`
= 500 × 1001
= 500500
Therefore, Sum of the first 1000 positive integer is 500500.
APPEARS IN
संबंधित प्रश्न
Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.
If the sum of the first n terms of an A.P. is `1/2`(3n2 +7n), then find its nth term. Hence write its 20th term.
Check whether -150 is a term of the A.P. 11, 8, 5, 2, ....
The first three terms of an AP are respectively (3y – 1), (3y + 5) and (5y + 1), find the value of y .
Find the sum of the following Aps:
i) 2, 7, 12, 17, ……. to 19 terms .
If the common differences of an A.P. is 3, then a20 − a15 is
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 =`[ ]`
For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?
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.
Write the sum of first n odd natural numbers.
If `4/5` , a, 2 are three consecutive terms of an A.P., then find the value of a.
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
Two A.P.'s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30th term is
Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
The term A.P is 8, 10, 12, 14,...., 126 . find A.P.
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.
The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.
If the sum of the first m terms of an AP is n and the sum of its n terms is m, then the sum of its (m + n) terms will be ______.
Find the middle term of the AP. 95, 86, 77, ........, – 247.
In a ‘Mahila Bachat Gat’, Kavita invested from the first day of month ₹ 20 on first day, ₹ 40 on second day and ₹ 60 on third day. If she saves like this, then what would be her total savings in the month of February 2020?
