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प्रश्न
Find the sum of three-digit natural numbers, which are divisible by 4
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` = 225
Now, Sn = `"n"/2 ("t"_1 + "t"_"n")`
∴ S225 = `225/2 (100 + 996)`
= `225/2 (1096)`
= 225 × 548
= 123300
∴ The sum of three digit natural numbers, which are divisible by 4 is 123300.
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संबंधित प्रश्न
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 ×(5 + 3)]
Find the sum of the following arithmetic progressions:
`(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y)`, .....to n terms
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Find the sum of all odd numbers between 100 and 200.
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
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Find the three numbers in AP whose sum is 15 and product is 80.
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.
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Find the sum of natural numbers between 1 to 140, which are divisible by 4.
Activity: Natural numbers between 1 to 140 divisible by 4 are, 4, 8, 12, 16,......, 136
Here d = 4, therefore this sequence is an A.P.
a = 4, d = 4, tn = 136, Sn = ?
tn = a + (n – 1)d
`square` = 4 + (n – 1) × 4
`square` = (n – 1) × 4
n = `square`
Now,
Sn = `"n"/2["a" + "t"_"n"]`
Sn = 17 × `square`
Sn = `square`
Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is `square`.
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