Question

the sum of integers from 1 to 300 which are divisible by 2 or 5​

Answer 1

Given : integers from 1 to 300 which are divisible by 2 or 5​

To find : Sum of integers

Solution :

integers from 1 to 300

Divisible by 2  

2 , 4  , 6  , .........................................., 300

Sum

= 2+ 4  + 6  + .........................................+300

= 2(1 + 2 + 3 +.............................+ 150)

= 2 ( 150)(151)/2

= 22650

Divisible by 5

5 , 10  , 15  , .........................................., 300

Sum

= 5+ 10 + 15  + .........................................+300

= 5(1 + 2 + 3 +.............................+ 60)

= 5 (60)(61)/2

= 9150

Both contains number divisible by 10

Divisible by 10

 10  , 20  , .........................................., 300

Sum

=   10 +20  + .........................................+300

= 10(1 + 2 + 3 +.............................+ 30)

= 10 (30)(31)/2

= 4650

sum of integers from 1 to 300 which are divisible by 2 or 5​

= 22650 + 9150 - 4650

=27150

27150  is   sum of integers from 1 to 300 which are divisible by 2 or 5​

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Answer 2

Given:

Find integers from 1 to 300 that are divisible by 2 or 5​

To find:

Sum of integers=?

Solution :

Formula:

$S=\frac{n}{2}[(a+l)]$

the number from 1 to 300, which is divisible by 2:

n=150, a=2, l=300

$\to S= \frac{150}{2}[2+300]$

        $= 75 \times 302\\\\ = 22,650$

the number from 1 to 300, which is divisible by 5:

n=60, a=5, l=300

$\to S= \frac{60}{2}[5+300]$

        $= 30 \times 305\\\\ = 9,150$

Now we calculate the value, which is not divisible by 10 so, the number from 1 to 300, which is not divisible by 10:

n=30, a=10, l=300

$\to S= \frac{30}{2}[10+300]$

        $= 15 \times 310\\\\ = 4,650$

The sum of 1 to 300 integer numbers which are divisible by 2 or 5 is:​

$= 22650 + 9150 - 4650\\=27150$

The final answer is "27,150".