Divide: 48xy4 - 72xy2 12xy2

Mathematics

1 answer:

Blizzard [7]3 years ago

6 0

Dude that is so unclear it is like driving with spry paint all over your windsheild

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What is the first term in a geometric sequence if the common ratio is − 2 and the sum of the first six terms is −105?

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$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
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r=-2\\
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S_6=-105
\end{cases}$

$\bf -105=a_1\left( \cfrac{1-(-2)^6}{1-(-2)} \right)\implies -105=a_1\left( \cfrac{1-(64)}{1+2} \right)
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-105=a_1\left( \cfrac{-63}{3} \right)\implies -105=a_1(-21)
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\cfrac{-105}{-21}=a_1\implies 5=a_1$

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