Question

Find the sum of 3 digit numbers not divisible by 7.

Answer 1

Answer:

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.]

Sum of all three digit numbers which are divisible by 7

= 105 + 112 + ..... + 994

Let 994 be the nth term of the given series.

∴ 994 = 105 + (n – 1) × 7

⇒ 7(n – 1) = 889

⇒ n – 1 = 127

⇒ n = 128

So, sum of all three digit numbers which are divisible by 7

∴ Sum of all three digit numbers which are not divisible by 7 = 494500 – 70336 = 424164

Answer 2

Step-by-step explanation:

sum of all three digit number which are not divisible by 7 (Sn)= sum of all three digit numbers(Sn1)-sum of all three digit numbers divisible by 7(Sn2)

sum of all three digit numbers,

100+101+102.....+999

but we have to find the value of n....

an = a+(n-1)d

999 = 100+(n-1)*1

999-100 = n-1

899+1 = n

900 = n

sum of all three digit numbers..{S1)

so we know that,

S1 = n/2(a+l)

S1 = 900/2(100+999)

S1 = 450*1099

S1 =494550

Now,sum of all three digit numbers divisible by 7....{S2}

105+112......+994

finding the value of n....

an =a+(n-1)d

994= 105+(n-1)*7

994-105=(n-1)7

889/7= n-1

127+1=n

128=n

now.....

S2 = n/2(a+l)

S2= 128/2(105+994)

S2=64(1099)

S2=70336

Now,sum of all three digit numbers not divisible by 7= sum of all three digit numbers- sum of all three digit numbers divisible by 7

or we can say

Sn= Sn1-Sn2

Sn=494550-70336

Sn=424214

Therefore,sum of all three digit numbers not divisible by 7 is 424214...

VERY IMPORTANT QUESTION