# Math Help - Partial Sum/Sequence questions...

1. ## Partial Sum/Sequence questions...

Obviously I'm making some sort of systematic error...any help is greatly appreciated!

15.) The number of cars sold weekly by a new auto dealership grows according to a linear growth model. The first week the dealership sold two cars $P_0=2$ and the second week the dealer ship sold six cars $P_1=6$

In the first 50 weeks, how many cars did the dealership sell?

My work:

$S_n=\frac{(P_0+P_{n-1})(n)}{2}$

$P_{n-1}=P_{49-1}=P_{48}$

$P_{48}=P_0+nd=2+48(4)=194$

$S_{49}=\frac{(2+194)(49)}{2}$

$S_{49}=4802$

17.) $5+8+11+14+...+299+302=?$ (100 terms)

My work:

$S_{99}=\frac{(5+299)(99)}{2}=15,048$

19.) $15+11+7+3+...$

Find the sum of the first 100 terms

My work:

$P_{98}=15+(-4)(98)=-377$

$S_{99}=\frac{(P_0+P_{n-1})(n)}{2}=\frac{(15+(-377))(99)}{2}=-17,919$

Like I said, I'm pretty sure it's a systematic error I'm making...I've tried it lots more way besides this, but I think this is the "most" correct way I've tried....any help will be wonderful. Thanks!!

2. Originally Posted by elizsimca

17.) $5+8+11+14+...+299+302=?$ (100 terms)

\begin{aligned}\underbrace{5+8+11+\cdots}_{100\tex t{ terms}}&=\sum_{n=0}^{99}\left\{5+3n\right\}\\
&=5(99+1)+3\cdot\frac{99\cdot{100}}{2}\\
&=15350\end{aligned}

Using $\sum_{n=0}^{N}c=c(N+1)$

and $\sum_{n=0}^{N}n=\frac{N(N+1)}{2}$

And
19.) $15+11+7+4+\cdots=?$

100 terms

Find the sum of the first 100 terms
\begin{aligned}\underbrace{15+11+7+4+\cdots}_{100\ text{ terms}}&=\sum_{n=0}^{99}\left\{15-4n\right\}\\
&=15(99+1)-4\cdot\frac{99\cdot100}{2}\\
&=-18300\end{aligned}

3. Originally Posted by Mathstud28
\begin{aligned}\underbrace{5+8+11+\cdots}_{100\tex t{ terms}}&=\sum_{n=0}^{99}\left\{5+3n\right\}\\
&=5(99+1)+3\cdot\frac{99\cdot{100}}{2}\\
&=15350\end{aligned}

Using $\sum_{n=0}^{N}c=c(N+1)$

and $\sum_{n=0}^{N}n=\frac{N(N+1)}{2}$

And

\underbrace{15+11+7+4+\cdots}_{100\text{ terms}}&=\sum_{n=0}^{99}\left\{15-4n\right\}\\
&=15(99+1)-4\cdot\frac{99\cdot100}{2}\\
&=-18300\end{aligned}
Mathstud,

So am I using an incorrect formula? Is the formula I tried to use on number 17 completely incorrect? That's the formula my professor gave us and I'm wondering if it was typed incorrectly because I'm getting all my partial arithmetic sums incorrect when I use that formula...when I do it your way, I get the correct answer....any thoughts?

Thanks

4. Originally Posted by elizsimca
Mathstud,

So am I using an incorrect formula? Is the formula I tried to use on number 17 completely incorrect? That's the formula my professor gave us and I'm wondering if it was typed incorrectly because I'm getting all my partial arithmetic sums incorrect when I use that formula...when I do it your way, I get the correct answer....any thoughts?

Thanks
No! You are in fact using the right formula ...but unfortunately you are putting in the wrong numbers

$S_{100}=\frac{\left(5+{\color{red}302}\right)\cdot {\color{red}100}}{2}=15350$

Dont worry those upper indexes always get people

5. Originally Posted by elizsimca
15.) The number of cars sold weekly by a new auto dealership grows according to a linear growth model. The first week the dealership sold two cars $P_0=2$ and the second week the dealer ship sold six cars $P_1=6$

In the first 50 weeks, how many cars did the dealership sell?

My work:

$S_n=\frac{(P_0+P_{n-1})(n)}{2}$

$P_{n-1}=P_{49-1}=P_{48}$

$P_{48}=P_0+nd=2+48(4)=194$

$S_{49}=\frac{(2+194)(49)}{2}$

$S_{49}=4802$

You are taking $n=50$ so you should be working out $S_{50}=\frac{(P_0+P_{49})(50)}2.$

6. Originally Posted by Mathstud28
No! You are in fact using the right formula ...but unfortunately you are putting in the wrong numbers

$S_{99}=\frac{\left(5+{\color{red}302}\right)\cdot{ \color{red}100}}{2}=15350$

Dont worry those upper indexes always get people

But if $P_0=$ Week 1...then wouldn't the 50th week be given by $P_{49}$?

Sorry, I'm having a dumb math moment....lol

7. Originally Posted by elizsimca
But if $P_0=$ Week 1...then wouldn't the 50th week be given by $P_{49}$?

Sorry, I'm having a dumb math moment....lol
But how many terms are there?

8. Originally Posted by Mathstud28
But how many terms are there?
touche'