Answer:
Sum of all multiples of 4 between 25 and 100 is 1116.
Step-by-step explanation:
Multiples of 4 between 25 and 100 = 28,32,36,40..............,96
let's check the series whether it is an arithmetic progression
a1 = 28 , a2 = 32 , a3 = 36 , a4 = 40
Common difference (d)=a2-a1=32-28 = 4
=a3-a2=36-32 = 4
=a4-a3=40-36 = 4
Common difference exists then the series of numbers is an Arithmetic progression.
To find number of terms :
a(a1) = 28 , d = 4 , l( last term ) = 96
l = a + (n-1)d
96 = 28 + (n-1)4
96 - 28 = (n-1)4
68 = (n-1)4
68/4 = (n-1)
17 = n - 1
17 + 1 = n
18 = n
Sum of all terms:
a = 28 , d = 4 , n = 18 , l = 96
Sn = n/2 ( a + l )
S18 = 18 / 2 (28 + 96)
S18 = 9 (124)
S18 = 1116
Therefore,Sum of all multiples of 4 between 25 and 100 is 1116.
<em>NOTE:</em>
<em>Here </em><em>100 </em><em>is </em><em>also</em><em> </em><em>a </em><em>multiple </em><em>of </em><em>4</em><em> </em><em>but </em><em>question</em><em> </em><em>is </em><em>asked </em><em>between</em><em> </em><em>2</em><em>5</em><em> </em><em>and </em><em>100 </em><em>so </em><em>100 </em><em>is </em><em>not </em><em>considered </em><em>in </em><em>multiples.</em>
