Question

Find the sum of all 3 digit numbers which are divisible by 8

Answer 1

Answer:

The sum of all 3 digit numbers divisible by 8 is 61376.

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Answer 2

➼Solution:-

⇒Step 1:

The first 3 digit number divisible by 8 is 104.

After 104, to find the next 3 digit number divisible by 8, we have to add 8 to 104. So the second 3 digit number divisible by 8 is 112.

In this way, to get the succeeding 3 digit numbers divisible by 8, we just have to add 8 as given below. 

Clearly, the above sequence of 3 digit numbers divisible by 8 forms an arithmetic sequence. 

And our aim is to find the sum of the terms in the above arithmetic sequence. 

⇒Step 2 :

In the arithmetic sequence

104, 112, 120, 128,...............................992,  

we have

⇒first term  =  104

⇒ common difference  =  8

⇒ last term  =  992

That is,

a  =  104

d  =  8

l  =  992

⇒Step 3 :

The formula to find the numbers of terms in an arithmetic sequence is given by

n = [(l - a) / d] + 1

Substitute a = 104, l = 992 and d = 8.

n  =  [(992 - 104) / 8] + 1

n  =  [888/8] + 1

n  =  111 + 1

n  =  112

So, number of 3 digit numbers divisible by 8 is 112.

⇒Step 4:

The formula to find the sum of 'n' terms in an arithmetic sequence is given by

=  (n/2)(a + l)

Substitute a = 104, d = 8, l = 992 and n = 112.

=  (112/2)(104 + 992)

=  56 x 1096

=  61376

So, the sum of all 3 digit numbers divisible by 8 is 61376.