Question

There are 20 consecutive even numbers. How much bigger is the sum of the 10 larger ones than the sum of the ten smaller ones?

Answer 1

Hey dear,

◆ Answer-

Sn'-Sn = 200

◆ Explaination-

Let a be first no in the series with common difference 2.

For first 10 numbers -

Sn = n/2 [2a + (n-1)d]

Sn = 10/2 [2a + (10-1)2]

Sn = 10a + 90

For next 10 numbers-

Sn' = n/2 [2(a+10d) + (n-1)d]

Sn' = 10/2 [2(a+10×2) + (10-1)2]

Sn' = 10a + 290

Therefore,

Sn'-Sn = (10a+290) - (10a+90)

Sn'-Sn = 200

Hence, sum of 10 larger numbers is bigger by 200 than those of smaller ones.

Hope this helps...