Advertisements
Advertisements
प्रश्न
Find the sum of the first 40 positive integers divisible by 3
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.
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
संबंधित प्रश्न
How many multiples of 4 lie between 10 and 250?
Determine the A.P. whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Find the sum of first 40 positive integers divisible by 6.
Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
Find the 6th term form the end of the AP 17, 14, 11, ……, (-40).
If 4 times the 4th term of an A.P. is equal to 18 times its 18th term, then find its 22nd term.
The sequence −10, −6, −2, 2, ... is ______.
In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.
Write the nth term of the \[A . P . \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]
The sum of n terms of two A.P.'s are in the ratio 5n + 9 : 9n + 6. Then, the ratio of their 18th term is
Let the four terms of the AP be a − 3d, a − d, a + d and a + 3d. find A.P.
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.
Find the common difference of an A.P. whose first term is 5 and the sum of first four terms is half the sum of next four terms.
The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.
Find the sum of the integers between 100 and 200 that are not divisible by 9.
Find the value of a25 – a15 for the AP: 6, 9, 12, 15, ………..
In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25th term of the A.P.
Rohan repays his total loan of ₹ 1,18,000 by paying every month starting with the first installment of ₹ 1,000. If he increases the installment by ₹ 100 every month, what amount will be paid by him in the 30th installment? What amount of loan has he paid after 30th installment?
The sum of the 4th and 8th term of an A.P. is 24 and the sum of the 6th and 10th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.
