find the sum of all integer from 1 to 500 which are multiples of 2 or 5
Answers
Answer:
ANSWER
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
Step-by-step explanation:
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