# Math Help - Series

1. ## Series

Find the sum of all even numbers between 2 & 200 inclusive, excluding those which are multiples of 3.

Sum of even numbers, is it means the series of
2 + 4 + 6 + ….+ 200?

Excluding multiples of 3, is it means
6 + 12 + 18 +....+ 198?

2. Originally Posted by geton
Find the sum of all even numbers between 2 & 200 inclusive, excluding those which are multiples of 3.

Sum of even numbers, is it means the series of
2 + 4 + 6 + ….+ 200?

Excluding multiples of 3, is it means
6 + 12 + 18 +....+ 198?
It effectively means (2 + 4 + 6 + ….+ 200) - (6 + 12 + 18 +....+ 198)

3. Originally Posted by mr fantastic
It effectively means (2 + 4 + 6 + ….+ 200) - (6 + 12 + 18 +....+ 198)
Yes I found my mistake. My mistake was n/3 [2a + (n-1)d] instead of n/2 [2a + (n-1)d].

Thank you.

4. Originally Posted by geton
Find the sum of all even numbers between 2 & 200 inclusive, excluding those which are multiples of 3.

Sum of even numbers, is it means the series of
2 + 4 + 6 + ….+ 200?

Excluding multiples of 3, is it means
6 + 12 + 18 +....+ 198?

{ $x$ :2≤ $x$ ≤200 }
$4,6,8,...,198 \quad A.P.$

$a=4$
$d=2$
$n=98$

$S_A=0.5n(a+l)$
$S_A=0.5(98)[(4)+(198)]$

$6,12,18,...,198 \quad A.P.$

$a=6$
$d=6$
$n=33$

$S_B=0.5n(a+l)$
$S_B=0.5(33)[(6)+(198)]$

$S_A-S_B$

5. Originally Posted by geton
Yes I found my mistake. My mistake was n/3 [2a + (n-1)d] instead of n/2 [2a + (n-1)d].

Thank you.
Between 2 and 200, that means 2 and 200 are not included right?

6. Originally Posted by SengNee
Between 2 and 200, that means 2 and 200 are not included right?
between 2 & 200 inclusive

7. Originally Posted by geton
Find the sum of all even numbers between 2 & 200 inclusive, excluding those which are multiples of 3.

Sum of even numbers, is it means the series of
2 + 4 + 6 + ….+ 200?

Excluding multiples of 3, is it means
6 + 12 + 18 +....+ 198?
Here is an easier way to sum.

$2+4+6 +\cdots +200 = 2(1+2+\cdots + 50) = 2\cdot \frac{50(51)}{2}=50(51)$

$6+12+18+\cdots +198 = 6(1+2+\cdots + 36) = 6\cdot \frac{36(37)}{2} = 3(36)(37)$