Question

(2) Sum of those integers from 1 to 500
which are multples of 2 as well as of 5.
500​

Answer 1

Answer:

75250

Step-by-step explanation:

N1: Number of terms from 1 to 500 which are multiples of 2 =250

N1:2,4,6,8............500

N2: Number of terms from 1 to 500 which are multiples of 5 =100

N2:5,10,15.......500

N3: Number of terms from 1 to 500 which are multiples of 10 (both 2 and 5) =50

N3:10,20,30...500

Sum of integers which are multiples of 2 from 1 to 500=

S

N1

=

2

N1

[2a+(N1−1)d]

S

N1

=

2

250

[2(2)+(250−1)2]

S

N1

=125[502]=62750

Sum of integers which are multiples of 5 from 1 to 500=

S

N2

=

2

100

[2(5)+(100−1)5]

S

N2

=50[505]=25250

Sum of integers which are multiples of 10 from 1 to 500=

S

N3

=

2

50

[2(10)+(50−1)10]

S

N3

=25[510]=12750

Hence, the sum of integers from 1 to 500 which are multiples of 2 or 5=

S

N1

+S

N2

−S

N3

=62750+25250−12750

=75250.

Sum =75250