Question

Find the sum of all even numbers from 1 to 350.

Answer 1

See the attachment for detail solution
Hope it will help you

Answer 2

The sum of all even numbers from 1 to 350 is 30800.

Given:

We have been given range from 1 to 350.

Solution:

Between the above range from 1 to 350, the even numbers are:

2, 4, 6, 8, 10, 12, 14...................350.  

The above is known as Arithmetic progression in which the first term is 2.

Let us denote terms as t.

$t_{1}=2$

Difference between terms $=\mathrm{t}_{2}-\mathrm{t}_{1}=4-2=2$

Number of terms between 1 and 350 $=\frac{350}{2}=175$.

Sum of the Arithmetic progression $=S_{n}=\frac{n}{2}[a+l]$

Whereas n = number of terms, a = first term and l = last term.

n = 175, a = 2, l = 350

Thus, $S_{175}=\frac{175}{2}[2+350]$

$=\frac{175}{2}[352]$

$=175 \times 176$

=30800.