Question

Find the sum of all natural numbers between 602 and 902 which are not divisible by 4

Answer 1

Answer:

The required sum is 168448

Step-by-step explanation:

First we find sum of all natural numbers which are divisible by 4

604, 608,............900

This is an A.P with a=604 and d=4

Number of terms,

$n=\frac{l-a}{d}+1$

$n=\frac{900-604}{4}+1$

$n=\frac{296}{4}+1$

$n=74+1$

$n=75$

Sum of natural numbers between 602 and 902 which are divisible by 4 is

$S_n=\frac{n}{2}[a+l]$

$S_{75}=\frac{75}{2}[602+902]$

$S_{75}=\frac{75}{2}[1504]$

$S_{75}=75*752$

$S_{75}=56400$

Now we find sum of all natural numbers from 603 to 901

$=603+603+........+901$

$=(1+2+......+901)-(1+2+.....+602)$

$=\frac{901*902}{2}-\frac{602*603}{2}$

$=(901*451)-(301*603)$

$=(901*451)-(301*603)$

$=406351-181503$

$=224848$

The required sum

=(sum of all natural numbers from 603 to 901)-(sum of all natural numbers between 602 and 902 which are divisible by 4)

=224848-56400

=168448

Answer 2

Answer:

The required sum is 168448

Step-by-step explanation:

Step-by-step explanation:

First we find sum of all natural numbers which are divisible by 4

604, 608,............900

This is an A.P with a=604 and d=4

Number of terms,

n=\frac{l-a}{d}+1n=

d

l−a

+1

n=\frac{900-604}{4}+1n=

4

900−604

+1

n=\frac{296}{4}+1n=

4

296

+1

n=74+1n=74+1

n=75n=75

Sum of natural numbers between 602 and 902 which are divisible by 4 is

S_n=\frac{n}{2}[a+l]S

n

=

2

n

[a+l]

S_{75}=\frac{75}{2}[602+902]S

75

=

2

75

[602+902]

S_{75}=\frac{75}{2}[1504]S

75

=

2

75

[1504]

S_{75}=75*752S

75

=75∗752

S_{75}=56400S

75

=56400

Now we find sum of all natural numbers from 603 to 901

=603+603+........+901=603+603+........+901

=(1+2+......+901)-(1+2+.....+602)=(1+2+......+901)−(1+2+.....+602)

=\frac{901*902}{2}-\frac{602*603}{2}=

2

901∗902

−

2

602∗603

=(901*451)-(301*603)=(901∗451)−(301∗603)

=(901*451)-(301*603)=(901∗451)−(301∗603)

=406351-181503=406351−181503

=224848=224848

The required sum

=(sum of all natural numbers from 603 to 901)-(sum of all natural numbers between 602 and 902 which are divisible by 4)

=224848-56400

=168448