Geometric Progression help please

[SabziiKumari]

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.

 

[soroban]

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,

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


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

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

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


\(\displaystyle \text{The first three terms are: }\;\frac{1}{29},\;-\frac{5}{29},\;\frac{25}{29}\)