Question

Sum of all the even numbers between 1 - 350 .

Answer 1

Hey buddy your answer is in the picture.

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Answer 2

Given,

The range of is 1 to 350.

To find,

The sum of all even numbers which are situated between the first and last number of the given range. (ie. 1 to 350)

Solution,

So, the range of the even numbers will look like this :

2,4,6,8,10......346,348

Now, surely the above mentioned range is in an AP or Arithmetic Progression. (Because, difference between two consecutive numbers in the given series is always constant.)

Let, first element of the AP = a

Last element of the AP = l

Difference between two consecutive numbers = d

Number of elements in the AP = n

Now, according to the available mathematical formula :

l = a+(n-1)d

348 = 2+(n-1)×2 [By putting respective values]

348 = 2+2n-2

348 = 2n

2n = 348

n = 174

So,there are 174 elements in the given AP.

Now,

Sum of even numbers = n/2 (a+l) = 174/2 × (2+348) = 87×350 = 30450

Hence,the sum of all even numbers between 1 to 350 is 30450. (Excluding 350)