Question

Find the sum of all natural numbers between 1 to 100 which are not multiples of 4.

Answer 1

bet^n 1 to 100 which are not multiples of 4
4,8,12.......100
t1=4,d=4,tn=100

tn=a+(n-1)×d
100=4+(n-1)×4
100-4/4=n-1
96/4=n-1
24=n-1
n=24+1
n=25

S25
=n/2(t1+tn)
=25/2(4+100)
=25/2×104
=25×52
=1300

the sum of all no. bet^n 1 to 100 which are multiple of 4 is 1300.

Answer 2

Answer:

3750

Step-by-step explanation:

first calculate sum of all numbers from 1 to 100

S100 = 100/2(2*1+(100-1)1)

S100=50(2+99)

S100=50*101=5050

now calculate sum of all numbers which are multiples of 4 from 1 to 100

AP: 4,8,12 .....100

an = a+(n-1)d

100= 4+(n-1)4

96/4=n-1

n=25

S= 25/2(2*4+(25-1)4)

S=25/2(8+24*4)

S=1300

now for the sum of all natural numbers from 1 to 100(including 1 and 100)which are not multiples of 4

S100-S = 5050-1300=3750 Ans.

note: in order to get sum excluding 1 and 100 then take no. between 1 and 100