Question

Find S15 for 1 + 1.5 + 2.25 + 3.375 +...

Answer 1

seems more like r = ?

Answer 2

r=1.5?

Answer 3

another parthkohli ;) ?

Answer 4

The Pattern is multiplying each one by 1.5.

Answer 5

yeah... parthkohli (2) :D

Answer 6

This is a geometric series with r = 1.5, as you mentioned.

Try using the summation formula to find the \(15\)th term.

Answer 7

*sigh* I made this account for some reasons. Anyway, yes, this is the gist of it.

Answer 8

291.92?

Answer 9

That's not exactly what I'm getting.

Answer 10

ill try again

Answer 11

http://www.wolframalpha.com/input/?i=%281+-+%281.5%29%5E%2815%29%29%2F%281+-+1.5%29

Answer 12

so 873? :) :)

Answer 13

I guess so.

Answer 14

would you help me with another one pleasee??

Answer 15

Surely.

Answer 16

I need to find the three geometric means between 1/2 and 8

Answer 17

There are many ways to do this - all of them similar.

One way is to define a geometric progression with the first term as 1/2 and the fifth term as 8.

Answer 18

ok :)?

Answer 19

All geometric progressions are in the form,\[a, ~ar, ~ar^2 \cdots ar^{n -1}\]We know that are geometric progression has the first term 1/2 and the last term 8. The three "geometric means" are actually the middle three terms that are in the geometric progression.

Our geometric progression is in the form\[1/2, ~~ r\cdot 1/2 , ~~ r^2 \cdot 1/2 , ~ ~ r^3 \cdot 1/2, ~ ~ r^4 \cdot 1/2\]

Answer 20

But we know for a fact that the fifth term is \(8\).

The fifth term is in the form \(r^4 \cdot 1/2\), which means\[r^4 \cdot \dfrac{1}{2} = 8 \implies r^4 = 16 \implies r = 2\]

Answer 21

Now that you know \(r\), you can easily calculate the three terms. Do you follow?

Answer 22

yes :)?

Answer 23

OK - what do you get?

Answer 24

1, 2, 4?

Answer 25

That's right!

Answer 26

THANKYOUUU!!!!

Answer 27

No problem!

And my main account is @ParthKohli - not this one, lol.

Answer 28

already a fan :) thanks!