Question

find the sum of find the sum of all even numbers from 1 to 350

Answer 1

The answer is:
Therefore sum of all even numbers from 1 to 350 is 30,800

Answer 2

Given:-

• An A.P 2, 4, 6, . . . . . , 350

To Find:-

• Sum of the A.P

Formula used:-

• $a_n= a+(n-1)d$

• $S_n=\dfrac{n}{2}(a+l)$

where,

• a = First term

• n = No. of terms

• d = Common Difference

• l = last term

• $a_n=\:n^{th}\:term$

• $S_n=\:Sum\:of\:n^{th}\:term$

Solution:-

Here,

• a = 2

• d = 4 - 2 = 2

• $a_n\:or\:l\:= 350$

Now,

$\implies\:a_n= a+(n-1)d$

$\implies\:350= 2+(n-1)2$

$\implies\:350= 2+2n-2$

$\implies\:2n=350$

$\implies\:n=\dfrac{350}{2}$

$\implies\:n=175$

Now using,

$\implies\:S_n=\dfrac{n}{2}(a+l)$

$\implies\:S_n=\dfrac{175}{2}(2+400)$

$\implies\:S_n=175×201$

$\implies\:S_n=35175$

Hence, The sum of all even numbers from 1 to 350 is 35175.

━━━━━━━━━━━━━━━━━━━━━━━━━

More Formulas:-

• $S_n=\dfrac{n}{2}[2a+(n-1)d]$

• $S_n=\dfrac{n}{2}[a+a+(n-1)d]$

• $S_n=\dfrac{n}{2}(a+a_n)$

━━━━━━━━━━━━━━━━━━━━━━━━━