Math, asked by Jayesh9960485, 1 year ago

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

Answers

Answered by BEJOICE
74
See the attachment for detail solution
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Jayesh9960485: I also got the same solution but when I checked the answer in textbook, I saw the answer is 30450. Hence I posted a question !
Answered by mindfulmaisel
49

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.

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