Question

Find the sum of all evan number from 1 to 350

Answer 1

Answer: 30,800

Step-by-step explanation:

To find : Sum of all even numbers between 1-350.

The number series of even numbers is 2, 4, 6... 350

First term a = 2

Common difference d = 2

Last term L= 350

Using the formula,

L = a + (n - 1)d

350=2 + ( n - 1 )2

350 = 2 + ( n - 1)2

348 = ( n - 1)2

348 = ( n - 1)2

174 = n - 1

n=175

Number of terms= 175

Now,

$\tt{S_{175} = \frac{n}{2} (a + L)}$

where a is first term, d is common difference, L is the last term and n is number of terms.

$\tt{S_{175}=\frac{175}{2}(2+350)}$

$\tt{S_{175}=\frac{175}{2}(352)}$

$\tt{S_{175}=175\times 176}$

$\tt{S_{175}=30800}$

Therefore, The sum of all even numbers between 1 to 350 is 30800.