Question

find the sum of all integers that are multiples of 4 from 1 to 150​

Answer 1

Step-by-step explanation:

We can solve this kind of problems in this way, from the numbers 1 to 150, we should be finding the smallest multiple of 4 and largest multiple of 4.

The smallest multiple of 4 is 4 itself, and the largest multiple of 4 is 148.

Go ahead and find the average of the smallest and largest multiple of 4 between 1 and 150, which is (4+148)/2 = 152/2= 76

Let’s find the total no.of numbers in between 1 and 150 which are multiple of 4. Can be found by ((largest multiple - smallest multiple)/4 ) + 1 = ((148–4)/4 + 1) = (144/4)+1 = 36+1 = 37

Sum is given by Average of Multiple * no.of multiples = 76*37 = 2812. There u go that’s your answer.

Happy Learning!

Answer 2

Answer:

The sum of all integers that are multiples of $4$ from $1$ to $150$ is $2812$

Step-by-step explanation:

Given:

To find the sum of all integers that are multiples of $4$ from $1$ to $150$.

The sequence will be

$4,8,12,...,148$

As this sequence is in A.P

The first term is $a=4$

The common difference is $d=4$

The last term is $l=148$

The last term can also be written as $a+(n-1)d$

By equating we get

$4+(n-1).4=148\\\\4n=148\\\\n=37$

There are $37$ terms we need to add

The sum of these terms is

$S_{37}=\frac{37}{2} [4+148]\\\\S_{37}=37*76\\\\S_{37}=2812$