Find the sum of all natural numbers between 300 and 600 which are divisible by 7
Answers
Step-by-step explanation:
this would be the answer
Given,
Natural numbers are between 300 and 600.
Divisible by 7.
To Find,
The sum of natural numbers between 300 and 600 can be divided by 7
Solution,
Given that,
Natural numbers are between 300 and 600.
They can be completely divided by 7.
So, the numbers are 301 to 599.
301 is divisible by 7.
595is divisible by 7.
The first number a₁ = 301
The last number aₙ = 595
The common difference, d =7
Therefore, we get an AP.
301,308,315,.......,595
Let's find the number of elements.
aₙ=a₁+(n-1)d
aₙ=301+(n-1)7
595=301+(n-1)7
595-301=(n-1)7
n=43
Let's find the sum of the 43 numbers.
S = (n/2)(2a₁+(n-1)d)
S = (43/2)(2*301+(43-1)7)
S = 21.5 (602+294)
S = 21.5 *896
S = 19264
19264 is the sum of all the natural numbers between 300and 600 which are divisibele by 7.