Multiples of $4$

Hello all,

As the range is [300,500], 300/4=75 , 500/4=125, both are divisible by 4,

therefore, a=300, Tn=last term= 500, d=4, we need to find the number of term(divisible by 4) of [300,500],

by applying arithmetic,

Tn= a+(n-1)d

500=300+(n-1)4

4n-4+300=500

4n=204

n=51(there 51 terms that divisible by 4 of [300,500],

Sn=n/2[2a+(n-1)d]----->find the sum of 51 terms,

S=51/2[600+(50)(4)]

=20 400

As requested S/100=20 400/ 100= 204,

therefore the answer is 204...

Thanks,YNWA....

First solve for the number of multiples of 4 in the interval given using the Arithmetic Sequence formula. Then after look for its summation by the Arithmetic Series formula. And of course divide it by 100.

the given problem forms the arithmatic sequences

300, 304,308,312, .....................................................500

first find out the nth term

Xn = a +(n -1)d

n = Xn -a+d/d

we know that a = 300 d = 4

n = 500 - 300 + 4 / 4 ==> n = 504 - 300 / 4 ==> 204 /4 =51

S = n / 2 ( 2a + ( n - 1 ) d )

S = 51 / 2 ( 600 + 200)

S = 20400

S /100 ==> 20400 / 100

          ===> 204Ans