Question

Find the sum of those integers from 1 to 500 which are multiples of 2 and 5.​

Answer 1

multiples of 2 from 1 to 500

2,4,6,....500

Lets use AP to find sum of this

a = 2

d = 4-2 =2

last term is 500 so

tn = a +(n-1)d= 2 + 2(n-1)= 500

2+ 2n -2 = 500

n = 250

so S2 = n/2 (first + last term)

= 250/2 *(2+500) = 125*502

same for multiple of 5

5, 10, 15....500

so Tn = a+ (n-1)*d

500 = 5 +5n-5

5n = 500

n = 100

So S5 = 100/2 ( 5 + 500) = 50 * 505

now special not we also have taken numbers which are divisible by 2 and 5 both 2 times

that is multiple of 10 are counted 2 time ' so we have to subtract it

lets do for 10

10 , 20, 30... 500

Tn = 10 + 10n -10 = 500

n = 500/10 = 50

so S_common = 50/2 (10+500) = 25* 510

now sum of all numbers which are multiple of 2 and 5 czn be given as

S = S2 + S5 - S_common

= 125*502 +50*505 - 25*510

= 75250

Answer 2

Answer:

12750 is the answer.....