Use the distributive property to express the sum of 48+84 as a multiple of 2 numbers with no common factor.

Mathematics

1 answer:

sesenic [268]3 years ago

6 0

48 + 84
12 (4+ 7)
12 times (11)

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How many terms are there in a geometric series if the first term is 4, the common ration is 3 and the sum of the series is 160

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

$\bf 160=4\left( \cfrac{1-3^n}{1-3} \right)\implies 160=4\left( \cfrac{1-3^n}{-2} \right)\implies 160=-2(1-3^n)
\\\\\\
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\\\\\\
81=3^n~~
\begin{cases}
81=3\cdot 3\cdot 3\cdot 3\\
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