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प्रश्न
Write the next term of the AP `sqrt(2) , sqrt(8) , sqrt(18),.........`
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उत्तर
The given AP is `sqrt(2) , sqrt(8) , sqrt(18) ,................`
On simplifying the terms, we get:
`sqrt (2) , 2 sqrt(2) , 3 sqrt(2) ,..................`
`Here , a= sqrt(2) and d = ( 2 sqrt(2) - sqrt(2)) = sqrt(2)`
∴ Next term `T_4 = a + 3d = sqrt(2) + 3 sqrt(2) = 4 sqrt(2) = sqrt(32)`
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संबंधित प्रश्न
Find the sum of first 40 positive integers divisible by 6.
Find the sum of the odd numbers between 0 and 50.
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)]
If the pth term of an A. P. is `1/q` and qth term is `1/p`, prove that the sum of first pq terms of the A. P. is `((pq+1)/2)`.
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Find the sum of the following arithmetic progressions:
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Which term of the sequence 114, 109, 104, ... is the first negative term?
Write the sum of first n even natural numbers.
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
The common difference of an A.P., the sum of whose n terms is Sn, is
Q.10
Q.16
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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`
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