find the sum of all natural numbers between 100 nd 500 which are divisible by 8
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All natural number between 100 and 500 which are divisible by 8 , are
104 , 112, 120 , 128 ,........... , 496
AP = 104,112,120,128.......,496
Here,
a = 104
D = (112-104) = 8
An = 496
An = a+(n-1) × d
496 = 104+(n-1) × 8
(n-1) × 8 = 496-104
(n-1) × 8 = 392
(n-1) = 392/8
n-1 = 49
n = 49+1
n = 50
Required sum = N/2 (a+An)
= 50/2 × (104+496)
= (25×600) = 15000
Hence,
The sum of all natural number lying between 100 and 500 which is divisible by 8 = 15000.
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