Find the sum of all two digit natural numbers which when divided by 7 yield 1as remainder .
To find the sum of all two-digit natural numbers that yield a remainder of 1 when divided by 7, we need to determine the range of numbers that satisfy this condition and then sum them up.
The first step is to find the smallest two-digit number that satisfies the given condition. Since we are looking for numbers that give a remainder of 1 when divided by 7, we can start by finding the smallest multiple of 7 that is larger than 10 (since we're looking for two-digit numbers):
7 x 2 = 14
So, 14 is the smallest two-digit number that satisfies the condition.
Next, we need to find the largest two-digit number that satisfies the condition. We can find this by finding the largest multiple of 7 that is smaller than 100:
7 x 14 = 98
So, 98 is the largest two-digit number that satisfies the condition.
Now, we have the range of numbers that satisfy the condition, which is from 14 to 98. To find the sum of these numbers, we can use the formula for the sum of an arithmetic series:
Sum = (n/2)(first term + last term)
In this case, the first term is 14, the last term is 98, and n is the number of terms in the series.
To find the number of terms, we can use the formula for the nth term in an arithmetic sequence:
n = (Last term - First term)/Common difference + 1
In this case, the common difference is 7 (since we are adding 7 to each term), so:
n = (98 - 14)/7 + 1
= 14
Now we have the number of terms (n = 14), the first term (a = 14), and the last term (l = 98). Let's substitute these values into the sum formula:
Sum = (n/2)(a + l)
= (14/2)(14 + 98)
= 7(112)
= 784
So, the sum of all two-digit natural numbers that yield a remainder of 1 when divided by 7 is 784.
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.
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