Advertisements
Advertisements
Question
Find the sum of the first 40 positive integers divisible by 5
Advertisements
Solution
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
RELATED QUESTIONS
How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?
Find the sum of the following arithmetic progressions:
a + b, a − b, a − 3b, ... to 22 terms
In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?
Find the sum of the first 15 terms of each of the following sequences having the nth term as
yn = 9 − 5n
Find the sum of 28 terms of an A.P. whose nth term is 8n – 5.
The 4th term of an AP is zero. Prove that its 25th term is triple its 11th term.
The angles of quadrilateral are in whose AP common difference is 10° . Find the angles.
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.
If `4/5 `, a, 2 are in AP, find the value of a.
Find the sum of first n terms of an AP whose nth term is (5 - 6n). Hence, find the sum of its first 20 terms.
Divide 207 in three parts, such that all parts are in A.P. and product of two smaller parts will be 4623.
What is the sum of first 10 terms of the A. P. 15,10,5,........?
If the sum of first p term of an A.P. is ap2 + bp, find its common difference.
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
The sum of first n odd natural numbers is ______.
If 18, a, b, −3 are in A.P., the a + b =
Which term of the AP 3, 15, 27, 39, ...... will be 120 more than its 21st term?
Solve for x: 1 + 4 + 7 + 10 + ... + x = 287.
Find the sum of odd natural numbers from 1 to 101.
If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be ______.
