Question

Help with geometric series, please?

Answer 1

Diana received 65 points on a project for school. She can make changes and receive three-tenths of the missing points back. She can do this 10 times . Create the formula for the sum of this geometric series, and explain your steps in solving for the maximum grade Diana can receive.

Answer 2

A lot of people have asked this question but each one got a different answer.

Answer 3

@dan815 @perl

Answer 4

@bibby I think you solved this problem?

Answer 5

You have the series:
65 + 3/10 * 65 + 3/10*( 3/10 * 65) + ..

Answer 6

Okay. I think I understand that. Where do I go from there?

Answer 7

This is equivalent to
$$ \Large {65 + 3/10 * 65 + (3/10)^2 * 65 + ... (3/10)^{10} * 65

}$$

Answer 8

Okay. Is this how who could get the maximum grade?

Answer 9

Or am I skipping ahead here?

Answer 10

Okay, how? What would I plug in?

Answer 11

Or can I just leave it at that? (Sorry if I'm rushing, I have to go soon)

Answer 12

we can plug it in

Answer 13

How?

Answer 14

$$ \Large \rm {

\sum _{k=0}^{10} 65\cdot (3/10)^k = \frac{65(1-(3/10)^{10+1})}{1-(3/10)}

}$$

Answer 15

also there was a typo in the formula above

$$
\Large \rm { \sum _{\color{red}{k=0}}^{n} a\cdot r^k = \frac{a(1-r^{k+1})}{1-r}

}

$$

Answer 16

Got it! Should I solve, too?

Answer 17

Wait why does k=0? @perl

Answer 18

@Nnesha

Answer 19

@perl please check this, it's my last problem for today!

Answer 20

Or can I just leave it at that? (Sorry if I'm rushing, I have to go soon)