Question

Chapter : AP
Class : 10

QFind -
sum of those integers from 1 to 500 which are multiples of 2 or 5​

Answer 1

Answer:

Sum of integers from 1-500 multiples of 2 or 5:

A.P can be formed:

Multiples of 2:

A.P= 2,4,6,...,500

a=2

d=4-2=2

l=500

n=500/2=250

S(n)= n/2(a+l)

= 250/2(2+500)

= 125(502)

=62750

Multiples of 5:

A.P= 5,10,15,...,500

a=5

d=10-5=5

l=500

n=500/5=100

S(n)= n/2(a+l)

= 100/2(5+500)

= 50(505)

= 25250

Now, The common terms in the multiples of both 2 & 5:

A.P= 10,20,30,...,500

a=10

d=20-10=10

l=500

n=500/10=50

S(n)= n/2(a+l)

= 50/2(10+500)

= 25(510)

= 12750

Now, The sum of integers from 1-500 multiples of 2 or 5:

= 62750+25250-12750

= 88000-12750

= 75250

hope it helps :)