Question

Find the sum of all integers from 100 to 200 which are divisible by 2 but not by 5.​

Answer 1

Step-by-step explanation:

Here an 2 APs are formed,

101,102,103,.....,199 ......(i)

and

105,110,115,.....,195 ......(ii)

in (i),

a=101, d=1 and tn=199

tn=a+(n-1)d

199=101+(n-1)1

199=101+n-1

199=100+n

n=99

Sn=n/2 {2a+(n-1)d}

=99/2 {2*101 +(99-1)1}

=99/2 {202+98}

=99/2 {300}

=99*150=14850

in (ii)

a=105, d=5 and tn=195

tn=a+(n-1)d

195=105+(n-1)5

(n-1)5=90

n-1=18

n=19

Sn=n/2 {2a+(n-1)d}

=19/2 {2*105 +(19-1)5}

=19/2 {210+90}

=19/2 {300}

=19*150=2850

therefore the sum of all number between 100 and 200 which are not divisible by 5=

the sum of all number between 100 and 200 - the sum of all number between 100 and 200 which are divisible by 5

=14850-2850

=12000

please mark as brainlist answer.