Advertisements
Advertisements
प्रश्न
Find the sum of three-digit natural numbers, which are divisible by 4.
Advertisements
उत्तर
The three-digit natural numbers divisible by 4 are
100, 104, 108, ......, 996
The above sequence is an A.P.
∴ a = 100, d = 104 – 100 = 4
Let the number of terms in the A.P. be n.
Then, tn = 996
Since tn = a + (n – 1)d,
996 = 100 + (n – 1)(4)
∴ 996 = 100 + 4n – 4
∴ 996 = 96 + 4n
∴ 996 – 96 = 4n
∴ 4n = 900
∴ n = `900/4`
∴ n = 225
Now, `S_n = n/2 (t_1 + t_n)`
∴ `S_225 = 225/2 (100 + 996)`
= `225/2 (1096)`
= 225 × 548
= 123300
∴ The sum of three-digit natural numbers, which are divisible by 4 is 123300.
APPEARS IN
संबंधित प्रश्न
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
If the term of m terms of an A.P. is the same as the sum of its n terms, show that the sum of its (m + n) terms is zero
A contract on a construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs. 200 for the first day, Rs. 250 for the second day, Rs. 300 for the third day, etc., the penalty for each succeeding day being Rs. 50 more than for the preceding day. How much money does the contractor have to pay as a penalty if he has delayed the work by 30 days?
The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceed the second term by 6, find three terms.
Find the middle term of the AP 10, 7, 4, ..., (–62).
The 9th term of an AP is –32 and the sum of its 11th and 13th terms is –94. Find the common difference of the AP.
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 the sum of P terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are
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 =
If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio
Q.11
Q.15
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
For an A.P., if t1 = 1 and tn = 149, then find Sn.
Activitry :- Here t1= 1, tn = 149, Sn = ?
Sn = `n/2 (square + square)`
= `n/2 xx square`
= `square` n, where n = 75
In a ‘Mahila Bachat Gat’, Sharvari invested ₹ 2 on first day, ₹ 4 on second day and ₹ 6 on third day. If she saves like this, then what would be her total savings in the month of February 2010?
The middle most term(s) of the AP: -11, -7, -3,.... 49 is ______.
The sum of all odd integers between 2 and 100 divisible by 3 is ______.
If the first term of an A.P. is 5, the last term is 15 and the sum of first n terms is 30, then find the value of n.
