Geometric progression question causing me problems.

[ivan77]

I am having trouble with this question even though i have guessed the answer which is correct btw. I want to know how i should solve such a question if it were ever more difficult than just guessing.

 

Here goes:Q The sum of the first 6 terms of a geometrical progression is 9 times the sum of the first 3. Find r. (r being the ratio).

 

If anybody could help i would be grateful, thanks.

[matt grime]

a+ar^2+ar^3+ar^4+ar^5 = 9(a+ar+ar^2)

divide by a

 

use the sum formla

 

(r^6-1)/(r-1)=3(r^3-1)/(r-1)

 

cancel the r-1

 

let y=r^3

 

y^2-1=3y-3

 

solve

[ivan77]

Thanks for the help matt, i knew it would be something simple.