Find the sum of all three digit numbers which are not divisible by 7
Answers
Answer:
I don't know
Step-by-step explanation:
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Answer:
424214
Step-by-step explanation:
Sum of all three digit numbers which are not divisible by 7
= Sum of all three digit numbers - Sum of all three digit numbers which are divisible by 7.
Sum of all three digit numbers
= 100+101+102+.....+999. The series is in A.P. [900 numbers]
Here, a = 100 , d =1 and n = 900
Sum of digits = 900 / 2 [2(100)+899]
= 450 * 1099
= 494550 .....(1)
Sum of all three digits numbers divisible by 7.
The first 3 digit number divisible by 7 is 105.
= 105, 112, 119, 126,..994
Here a first term = 105, common difference d= 7, last term n = 994
The formula to find the numbers of terms in an A.P n = [(l-a)/d] + 1
Substituting a = 105, l = 994 and d = 7
n = [(994-105)/7]+1
n = [889/7]+1 = 127 + 1
n = 128
The formula to find the sum of "n" terms in an A.P is = n/2{a+l}
Substituting a = 105, d = 7, l = 994 and n = 128, we get
= 128/2{105+994}
= 64 * 1099
= 70336 ....(2)
Hence, the sum of all 3 digit numbers divisible by 7 is 70336.
so, (1) - (2)
= 494550 - 70336
= 424214
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