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
Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.
Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
How many terms of the series 54, 51, 48, …. be taken so that their sum is 513 ? Explain the double answer
Find the sum given below:
34 + 32 + 30 + ... + 10
In an AP: Given a = 5, d = 3, an = 50, find n and Sn.
Show that a1, a2,..., an... form an AP where an is defined as below:
an = 9 − 5n
Also, find the sum of the first 15 terms.
Find the sum of first 8 multiples of 3
Find the 12th term from the end of the following arithmetic progressions:
3, 5, 7, 9, ... 201
Find the sum of the following arithmetic progressions:
`(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y)`, .....to n terms
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.
Find the sum of all multiples of 9 lying between 300 and 700.
Write an A.P. whose first term is a and the common difference is d in the following.
a = 10, d = 5
The sum of n terms of an A.P. is 3n2 + 5n, then 164 is its
The sum of first 20 odd natural numbers is
Let the four terms of the AP be a − 3d, a − d, a + d and a + 3d. find A.P.
Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.
If an = 3 – 4n, show that a1, a2, a3,... form an AP. Also find S20.
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 first 17 terms of an AP whose 4th and 9th terms are –15 and –30 respectively.
If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
