Advertisements
Advertisements
Question
Find the sum of the first 40 positive integers divisible by 3
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.
First 40 positive integers divisible by 3
n = number of terms
First 40 positive integers divisible by 3
So, we know that the first multiple of 3 is 3 and the last multiple of 3 is 120.
Also, all these terms will form an A.P. with the common difference of 3.
So here,
First term (a) = 3
Number of terms (n) = 40
Common difference (d) = 3
Now, using the formula for the sum of n terms, we get
`S_n = 40/2 [2(3) + (40 - 1)3]`
= 20[6 + (39)3]
= 20(6 + 117)
= 20(123)
= 2460
Therefore, the sum of first 40 multiples of 3 is 2460
APPEARS IN
RELATED QUESTIONS
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
Find the sum of first 51 terms of an A.P. whose 2nd and 3rd terms are 14 and 18 respectively.
If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, find the AP
The sum of the first n terms in an AP is `( (3"n"^2)/2 +(5"n")/2)`. Find the nth term and the 25th term.
Find four consecutive terms in an A.P. whose sum is 12 and sum of 3rd and 4th term is 14.
(Assume the four consecutive terms in A.P. are a – d, a, a + d, a +2d)
In an A.P., the first term is 22, nth term is −11 and the sum to first n terms is 66. Find n and d, the common difference
The sum of first 9 terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1 : 2. Find the first and 15th term of the A.P.
The sum of first n terms of an A.P. is 5n − n2. Find the nth term of this A.P.
The sum of first n terms of an A.P is 5n2 + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P.
The sum of first n odd natural numbers is ______.
The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals
The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.
In an A.P. a = 2 and d = 3, then find S12
What is the sum of an odd numbers between 1 to 50?
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 ______.
The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.
Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77.
Find the sum of the integers between 100 and 200 that are not divisible by 9.
If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.
k + 2, 2k + 7 and 4k + 12 are the first three terms of an A.P. The first term of this A.P. is ______.
