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Yogita Ingle 5 years, 2 months ago
Let the number of terms required to make the sum of 636 be n and common difference be d.
Given Arithmetic Progression : 9 , 17 , 25 ....
First term = a = 9
Second term = a + d = 17
Common difference = d = a + d - a = 17 - 9 = 8
From the indentities of arithmetic progressions, we know : -
, where
is the sum of first term to nth term of the AP, a is the first term, d is the common difference and n is the number of terms of AP.
In the given Question, sum of APs is 636.
Therefore,
= > 4n² + 5n - 636 = 0
= > 4n² + ( 53 - 48 )n - 636 = 0
= > 4n² + 53n - 48n - 636 = 0
= > 4n² - 48n + 53n - 636 = 0
= > 4n( n - 12 ) + 53( n - 12 ) = 0
= > ( n - 12 )( 4n + 53 ) = 0
By Zero Product Rule,
= > n - 12 = 0
= > n = 12
Hence,
Number of terms of the AP [ 9 , 17 , 25 ] which are required to make the sum of 636 is 12.
Posted by Yash Mishra 5 years, 2 months ago
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Yogita Ingle 5 years, 2 months ago
here a= 105
l= 994
n=?
d= 7
so
994 = 105+(n-1) 7
= 105+7n-7
994= 98+7n
994-98 = 7n
896/7 = n
n= 128
so 128 three digit numbers are divisible by 7
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Posted by Yash Mishra 5 years, 2 months ago
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Posted by ♦ Omkar Jadhav ♦ 5 years, 2 months ago
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Yogita Ingle 5 years, 2 months ago
Given, a=5,d=3,an=50
⇒a+(n−1)d=50
⇒5+(n−1)3=50
⇒5+3n−3=50
⇒3n=48
⇒n=16
∴S16=216[2a+(16−1)d]
=8[2×5+15×3]
=440
Hence, n=16,S16=440
Posted by Vinay Kumar 5 years, 2 months ago
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Yogita Ingle 5 years, 2 months ago
Factors of 144 = 2×2×2×2×3×3
Factors of 180 = 2×2×3×3×5
Factors of 192 = 2×2×2×2×2×2×3
Common factors of 144, 180, 192 = {2,2,3}
LCM (144,180,192) =
2×2×2×2×2×2×3×3×5 = 2880
So, HCF(144,180,192) = 2×2×3 = 12.
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The invisible man (Griffin) first became visible after he slipped into a big London store for keeping warm and overslept there while wearing some clothes taken from the store. To escape, he removed his clothes, becoming invisible. Thus he became homeless and was wandering the streets of London.
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Riya Philip 5 years, 2 months ago
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