Sequences and Series HELP!

[KingAce]

These are two problems I was given on last week's test. I got the answers wrong, and would really like to know how to do it. The problems are as follows:

1) What's the sum of all 3 digit numbers not divisible by 9?

2) (this ones a bit simpler) What's the sum of all 3 digit numbers that are a multiple of 3?

I'd write out the work that I did, but my teacher scribbled it all out.. and wrote nothing in its place :?
Please help!

 

[soroban]

Hello, KingAce!

2) (This one's a bit simpler.) What's the sum of all 3-digit numbers that are a multiple of 3?

\(\displaystyle \text{You want: }\:S \;=\;102 + 105 + 108 + \hdots + 999\)

\(\displaystyle \text{This is an arithmetic series with first term }a = 102\)

. . \(\displaystyle \text{common difference }d = 3\text{, and }n = 300\text{ terms.}\)

1) What's the sum of all 3-digit numbers not divisible by 9?

\(\displaystyle \text{Find the sum of }all\text{ 3-digit numbers: }\;S_1 \;=\;100 + 101 + 102 + \hdots + 999\)

\(\displaystyle \text{This is an arithmetic series with first term }a = 100\)

. . \(\displaystyle \text{common difference }d = 1\text{, and }n = 900\text{ terms.}\)


\(\displaystyle \text{Find the sum of all 3-digit numbers that }are \text{ divisible by 9: } \:S_2 \;=\;108 + 117 + 126 + \hdots + 999\)

\(\displaystyle \text{This is an arithmetic series with first term }a = 108\)

. . \(\displaystyle \text{common difference } d = 9\text{, and }n= 100\text{ terms.}\)


\(\displaystyle \text{The answer is: }\:S_1 - S_2\)

 

[stapel]

These are two problems I was given on last week's test.

What formulas were you given in class for sequences and series? :?:

And do you see now the importance of learning, even memorizing, them before the test? :wink:

I'd write out the work that I did, but my teacher scribbled it all out.. and wrote nothing in its place

My gracious! That's extremely odd behavior: taking a dark marker to completely blot out a student's work -- and to no particular purpose! Why on earth go to so much effort for no apparent reason?!? Does your instructor always seem this irrational and unbalanced? :shock:

But I'm sure you have some basic understanding of the questions and the concepts, so you can at least reply with how you'd do it now (which will likely be very close to how you did it then), and we can work from there. :idea:

Please be complete. Thank you!

Eliz.