Arithmetic Sequences

**damaster** · June 14th 2008, 04:41 PM

This is a question I really don't get. I've tried all the things i can think of, and the only clue i have is: Arithmetic Sequences (this is a topic I'm horrible at).

The problem is

Find the sum of all positive integers not greater than 10000 that are divisible by either 3 or 11 but not by both of them.'
Can you please help me soon????
Tkx
Mikhael

**sean.1986** · June 14th 2008, 04:44 PM

It's all the numbers divisible by 3 or 11 but NOT divisible by 33. Does that help?

**sean.1986** · June 14th 2008, 04:48 PM

So...

S3333, a = 3, d = 3

S909, a = 11, d = 11

Add those two answers together then subtract...

S303, a = 33, d = 33

**Soroban** · June 14th 2008, 06:46 PM

Hello, Mikhael!

We need the formula for the sum of an arithemtic series.

The sum of the first n terms is: . $S_n \:=\:\frac{n}{2}\bigg[2a + (n-1)d\bigg]$

. . where: $a$ = first term, $d$ = common difference.

Find the sum of all positive integers not greater than 10000
that are divisible by either 3 or 11 but not by both of them.

Sum of multiples of 3: . $S_3 \;=\; 3 + 6 + 9 + \hdots + 9999$
This is an arithmetic series with: . $a = 3,\;\; d = 3,\;\; n = 3333$
Its sum is: . $S_3 \:=\:\frac{3333}{2}\bigg[2(3) + 3332(2)\bigg] \:=\:16,668,333$

Sum of multiples of 11: . $S_{11} \;=\;11 + 22 + 33 + \hdots + 9999$
This is an arithmetic series with: . $a = 11,\;\;d=11\;\;n = 909$
Its sum is: . $S_{11} \;=\;\frac{909}{2}\bigg[2(11) + 908(11)\bigg] \;=\;4,549,545$

Sum of multiples of 33: . $S_{33} \;=\;33 + 66 + 99 + \hdots + 9999$
This is an arithmetic series with: . $a = 33,\;\;d = 33,\;<br /> \;n = 303$
Its sum is: . $S_{33} \;=\;\frac{909}{2}\bigg[2(33) + 302(33\bigg] \;=\;1,519,848$

The desired sum is: . $S_3 + S_{11} - 2(S_{33}) \;=\;\boxed{18,178,182}$

**sean.1986** · June 14th 2008, 07:46 PM

Shouldn't that be 303/2 for the 3rd one?

And why do you subtract twice the sum of the multiples of 33?

Thread: Arithmetic Sequences

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