Find the sum of all integers between 200 and 400 that are divisible by 6.
Answers
We need to find least number and greatest number divisible by 7 between 200 and 400.
Then we'll form an A.P with,
a = least \: term \: divisible \: by \: 7a=leasttermdivisibleby7
a_n \: or \: lanorl = greatest \: term \: divisible \: by \: 7greatesttermdivisibleby7
d = 7d=7
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Now, divide 400 by 7.
If you don't get any remainder then 400 is divisible by 7 and hence largest divisible number but if you get a remainder (which you will), then subtract the remainder from 400 to get largest number.
In this case, we get remainder = 1
Subtracting remainder from 400 = 400-1 = 399
Hence, largest number divisible by 7 is 399
=> \boxed{\mathsf{l = 399}}l=399 ✔️
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Now we'll divide 200 by 7.
This time if we get a remainder not equal to 0 then we'll subtract it from 200 and add 7.
The remainder we get is 4.
Now,
=> 200 - 4 + 7
=> 200 + 3
=> \boxed{\mathsf{ a = 203}}a=203 ✔️
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Now,
We know that,
a = 203
l = 399
d = 7
n = ?
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Using the formula,
✅\boxed{\mathbf{a_n = a + (n-1)d}}an=a+(n−1)d ✅
=> \mathsf{399 = 203 + (n-1)7}399=203+(n−1)7
=> \mathsf{399 - 203 = (n-1)7}399−203=(n−1)7
=> \mathsf{196 = (n-1)7}196=(n−1)7
=> \mathsf{\frac{196}{7} = n - 1}7196=n−1
=> \mathsf{ n - 1 = 28}n−1=28
=> \boxed{\mathsf{n = 29}}n=29 ✔️
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