Geometric Progression help please

SabziiKumari

New member
Joined
Jan 24, 2010
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19
the common ratio of GP is -5
the sum of the first seven terms of the progression is 449.
find first three terms,

for this would i put given information into the sum of GP
im stuck on the method.

i tried making the method = 449 .

then putting the common ratio into it to find a , but it doesnt seem to come out right.
 
Hello, SabziiKumari!

The common ratio of GP is -5
The sum of the first seven terms of the progression is 449.
Find first three terms,

The sum of the first n terms of a GP is:   Sn=arn1r1\displaystyle \text{The sum of the first }n\text{ terms of a GP is: }\;S_n \:=\:a\,\frac{r^n-1}{r-1}
. . where a is the first term, r is the common ratio.\displaystyle \text{where }a\text{ is the first term, }r\text{ is the common ratio.}


We are given: r=5,  n=7,  S7=449\displaystyle \text{We are given: }\:r = -5,\;n = 7,\;S_7 \:=\:449

So we have:   449  =  a(5)71(5)1\displaystyle \text{So we have: }\;449 \;=\;a\,\frac{(-5)^7 - 1}{(-5) - 1}

Then:   a781266=44913021a=449a=44913021=129\displaystyle \text{Then: }\;a\,\frac{-78126}{-6} \:=\:449 \quad\Rightarrow\quad 13021a \:=\:449 \quad\Rightarrow\quad a \:=\:\frac{449}{13021} \:=\:\frac{1}{29}


The first three terms are:   129,  529,  2529\displaystyle \text{The first three terms are: }\;\frac{1}{29},\;-\frac{5}{29},\;\frac{25}{29}

 
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