Advertisements
Advertisements
प्रश्न
Find the sum of the first 40 positive integers divisible by 5
Advertisements
उत्तर
In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of n terms of an A.P.,
`S_n = n/2 [2a + (n -1)d]`
Where; a = first term for the given A.P.
d = common difference of the given A.P.
n = number of terms
First 40 positive integers divisible by 5
So, we know that the first multiple of 5 is 5 and the last multiple of 5 is 200.
Also, all these terms will form an A.P. with the common difference of 5.
So here,
First term (a) = 5
Number of terms (n) = 40
Common difference (d) = 5
Now, using the formula for the sum of n terms, we get
`S_n = 40/2 [2(5) = (40 - 1)5]`
= 20[10 + (39)5]
= 20(10 + 195)
= 20(205)
= 4100
Therefore, the sum of first 40 multiples of 3 is 4100
APPEARS IN
संबंधित प्रश्न
Find the sum of first 20 terms of the following A.P. : 1, 4, 7, 10, ........
The sum of n, 2n, 3n terms of an A.P. are S1 , S2 , S3 respectively. Prove that S3 = 3(S2 – S1 )
If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is, S1)? What is the sum of the first two terms? What is the second term? Similarly, find the 3rd, the 10th, and the nth terms.
Find the sum of the first 40 positive integers divisible by 3
If the 8th term of an A.P. is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.
A sum of ₹2800 is to be used to award four prizes. If each prize after the first is ₹200 less than the preceding prize, find the value of each of the prizes
If an denotes the nth term of the AP 2, 7, 12, 17, … find the value of (a30 - a20 ).
How many terms of the A.P. 21, 18, 15, … must be added to get the sum 0?
In an A.P. the 10th term is 46 sum of the 5th and 7th term is 52. Find the A.P.
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 − S10)
Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − kSn−1 + Sn−2, then k =
Show that a1, a2, a3, … form an A.P. where an is defined as an = 3 + 4n. Also find the sum of first 15 terms.
If a = 6 and d = 10, then find S10.
Find the sum of odd natural numbers from 1 to 101.
If the numbers n - 2, 4n - 1 and 5n + 2 are in AP, then the value of n is ______.
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.
In an AP, if Sn = n(4n + 1), find the AP.
If the last term of an A.P. of 30 terms is 119 and the 8th term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.
Three numbers in A.P. have the sum of 30. What is its middle term?
