Question

Find the 10th partial sum of

Answer 1

@mathmale

Answer 2

Your best bet involves 1) identifying the common ratio of this geometric series and (2) identifying the first term of this series.

r = common ratio = ?

a = first term = ?

Answer 3

r=-5i?
a=2?

Answer 4

Once you have correctly identified these, we can move forward to finding the 10th sum of this geometric series.

Answer 5

That 'i' is a counter and is not part of the common ratio.

Answer 6

how do i find that

Answer 7

Regarding the first term, montverde, let i=1 and calculate the first term.

Answer 8

Unfortunately, it's not 2.

Answer 9

-3?

Answer 10

Yes, that's right. So, a=-3. Now, regarding the common ratio: Pls try again. Supposing we start with the first term, a=-3. What would the next term of this geom series be?

Answer 11

The summand of this geometric series is -5i+2. Try re-writing it as 2-5I.

Let i = 1, 2, 3, 4, 5, ...
What are the terms of the series for these i values?

Next, try again to identify the common ratio, r.

Answer 12

-8??

Answer 13

If i=1, the first term is 2-5(1) = -3, as you have already correctly stated.

What is the next term? i=2. Yes, it's -3 -5 = -8.

What is the common ratio, r?

r=?

Answer 14

2.6?

Answer 15

I had to stop for a moment to digest where this discussion is going.

The easiest (but not necessarily best) way to figure out the 10th partial sum would be to write out the first 10 terms and then add them up.

We'd get -3, -8, -13, -18, (and 6 more).

I should have noticed earlier that the problem would be clearer if we were to separate it into two parts:

\[\sum_{i=1}^{n}2+\sum_{i=1}^{n}(-5)i\]

Answer 16

-23,-28,-33,-38,-43,-48

Answer 17

yay i got it
it's -255

Answer 18

Remember, montverde: all of the terms of this series are negative.
Again, you could write out all 10 terms and then add them together.

Yes, it's -255. Note that because that -5 is negative, your sum MUST be negative also.

Answer 19

yes I understand it now, thank you so much you are the best

Answer 20

thanks, montverde, hope to work with you again soon!

Answer 21

Your result is definitelyl correct. I made a mistake earlier, however, in stating this this was a geometric series; it is not. It's an arithmetic series.