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C2 geometric series question

The first three terms of a geometric series are 4p, (3p + 15) and (5p + 20) respectively,where p is a positive constant.

Show that 11p2 – 10p – 225 = 0

Eh?
Original post by jessyjellytot14
The first three terms of a geometric series are 4p, (3p + 15) and (5p + 20) respectively,where p is a positive constant.

Show that 11p2 – 10p – 225 = 0

Eh?


Well, what does your gut instinct tell you to do? :tongue:

Hint:

Spoiler

(edited 7 years ago)
for any GP there is a way of finding the common ratio r using consecutive terms...
Reply 3
Avatar for Zacken
Zacken
22
Original post by jessyjellytot14
The first three terms of a geometric series are 4p, (3p + 15) and (5p + 20) respectively,where p is a positive constant.

Show that 11p2 – 10p – 225 = 0

Eh?


What do you know about consecutive terms in a geometric series? They have a common ratio.

The ratio of the second term to the first is the same as the ratio of the third term to the second, etc...

So u3u2=r=u2u1\frac{u_3}{u_2} = r = \frac{u_2}{u_1}. Here we have: ?3p+15=3p+15?\frac{?}{3p+15} = \frac{3p+15}{?}, now multiply out and simplify into the given quadratic.
Original post by SeanFM
Well, what does your gut instinct tell you to do? :tongue:

Hint:

Spoiler



I'll try doing ar/a = ar2/ar
Original post by jessyjellytot14
I'll try doing ar/a = ar2/ar


Update: It worked :smile:
Reply 6
Avatar for Zacken
Zacken
22
Original post by jessyjellytot14
Update: It worked :smile:


Well done! :woo:

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