Asked by Anonymous

Find the sum of all two digit natural numbers which when divided by 7 yield 1as remainder .
Answered by Reiny
What are two digit natural numbers which when divided by 7 yield 1as remainder ?
Well the smallest one is 15, and the largest is 99
They are 15, 22, .... 92, 99

They form an arithmetic sequence.
where a = 15, d = 7, term(n) = 99
Find how many terms there are, then find Sum(n) using your sum formula
Let me know what answer you get.
Answered by muhammed
we can simply show that 8 / 7 = 1 and the remainder is 1
and to keep the remainder equals to 1 we will add multiple of 7 to the number 8 which will always gives a remainder equals to 1
we need only the 2 digit numbers but 8 is one digit number so we won't take it into account
hence we will start from 8+7 =15 and 15 is two digit number
so sum = 15+22 +29+36+43+50+57+64741+71+78+85+92+99=741
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