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itsmichelle29
 one year ago
What is the sum of a 7term geometric series if the first term is −6, the last term is −24,576, and the common ratio is 4?
−32,766
−19,662
19,662
32,766
itsmichelle29
 one year ago
What is the sum of a 7term geometric series if the first term is −6, the last term is −24,576, and the common ratio is 4? −32,766 −19,662 19,662 32,766

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2You are given that: \(\large\color{black}{ \displaystyle a_1=6 }\) \(\large\color{black}{ \displaystyle a_7=24576 }\) (and you are are also given the this series is geometric).  Really, you don't need to know the value of the common ratio r, because you can find it yourself based on the given \(a_1\) and \(a_7\) \(\large\color{black}{ \displaystyle a_n=a_1\cdot {\rm r}^{n1} }\) (i am sure you have seen that before:D ) \(\large\color{black}{ \displaystyle a_7=a_1\cdot {\rm r}^{71} }\) \(\large\color{black}{ \displaystyle a_7=a_1\cdot {\rm r}^{6} }\) \(\large\color{black}{ \displaystyle 24576=(6)\cdot {\rm r}^{6} }\) \(\large\color{black}{ \displaystyle 4096={\rm r}^{6} }\) \(\large\color{black}{ \displaystyle \sqrt[6]{4096}=\rm r }\) \(\large\color{black}{ \displaystyle4=\rm r }\) 

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2But, they gave you the value of r, which makes it even easier.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2\(\large\color{black}{ \displaystyle {\rm S}_k=\frac{A_1\left(1{\rm r}^k\right)}{1{\rm r}}}\) This is the sum of a sequence that starts from \(a_1\), and ends on \(a_k\) (in other words for k number of terms)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2now, just plug in your given information \(k=7\) (since 7 is the last term) \(A_1=6\) \(\rm r=4\) and then evaluate this sum

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2ok, you are welcome, if you want. If you have any questions, then please ask.
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