Find the Sum of all natural number between 200 and 300 which is divisible by 7
Answers
so a= 203
d= 7
a(n) =294
a(n) = a+(n-1)d
294 = 203 + (n-1)7
294 = 203 +7n-7
294 = 196 + 7n
294-196 = 7n
98 =7n
98/7 =n
14 = n
s(n) = n/2[2a+(n-1)d]
s(14) =14/2[2×203 +(14-1)7]
= 7(406+13×7)
= 7(406+91)
= 7 (497)
= 3,479
So the sum is equal to 3,479
Given:
The natural numbers between 200 and 300
To find:
The sum of all natural numbers between 200 and 300 divisible by 7
Solution:
The sum of all natural numbers between 200 and 300 divisible by 7 is 3,479.
We can calculate the sum by following the given steps-
We know that the smallest and largest natural number between 200 and 300 that are also divisible by 7 is 203 and 294, respectively.
The sequence becomes 203, 210, and so on till 294.
So, an A.P. is formed.
The first term, a=203
The last term, l=294
The common difference, d=7
The number of terms, n=(last term-first term)/common difference+1
n=(294-203)/7+1
n=91/7+1
n=13+1=14 terms
The sum of the A.P. can be obtained by using the following formula-
Sum of all such natural numbers=n/2×(a+l)
On putting the values,
Sum=14/2(203+294)
=7(497)
=3,479
Therefore, the sum of all natural numbers between 200 and 300 divisible by 7 is 3,479.