hello :D

here's the question I need a hand with

Find the first three terms of a geometric progression where all terms are positive, S4 (the sum to four terms) = 21 2/3 and the sum to infinity = 27

thanks in advance, all help is much appreciated

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- Oct 21st 2008, 04:30 AMlisteningintentlygeometric progression problem
hello :D

here's the question I need a hand with

Find the first three terms of a geometric progression where all terms are positive, S4 (the sum to four terms) = 21 2/3 and the sum to infinity = 27

thanks in advance, all help is much appreciated - Oct 21st 2008, 05:04 AMADARSH
Find the first three terms of a geometric progression where all terms are positive, S4 (the sum to four terms) = 21 2/3 and the sum to infinity = 27

The formulas used for GP

Sn=a(1-(r^n))/(1-r) for n terms...(2)

and for infinite terms

Si=a/(1-r) for 0<r<1.......(1)

a=1st term

r=constant ratio

use it in above

put (1) in (2) for n= 4 to get r and thus a

further use (2) to find the terms reqd (Cool)

- Oct 21st 2008, 05:07 AMSoroban
Hello, listeningintently!

Quote:

Find the first three terms of a geometric progression

where all terms are positive, , and

. . Sum of the first terms: .

. . Sum to infinity: .

The sum of the first four terms is .[1]

The sum to infinity is 27: . .[2]

Substitute [2] into [1]: .

. .

Substitute into [2]: .

Therefore, the first three terms are: .