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Find the number of terms in the sequence.

 

-18, 36,-72,...,9437184

 May 4, 2021
 #1
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-1

Let's focus on every other number. 
We have: 36, 90, 144, ... 9437184.

The common difference is 54, so let's set every to a multiple of 54.

54, 108, 162, ... 9437202.

Dividing these terms by 54, we get:

1,2,3,...174763.

Remember, we are counting every other number, so there are really:

174763 * 2 = 349526 terms in the sequence.

 May 4, 2021
 #2
avatar+26135 
+2

Find the number of terms in the sequence.
\(-18,~ 36,~ -72,~\ldots ~,~9437184\)

 

My attempt:

\(\begin{array}{|r|rl|} \hline \text{sequence} & : 9 \\ \hline -18 & -2 & = (-2)^1 \\ \hline 36 & 4 & = 2^2 \\ \hline -72 & -8 & = (-2)^3 \\ \hline \ldots & \ldots & \ldots \\ \hline 9437184 & 1048576 & = 2^{20} \\ \hline \end{array}\)

 

\(\text{Formula:}\\ \begin{array}{|rcll|} \hline \mathbf{a_n} &=& \mathbf{9*(-2)^n} \\ a_{20} &=& 9*(-2)^{20} \\ a_{20} &=& 9*2^{20} \\ a_{20} &=& 9*1048576 \\ \mathbf{a_{20}} &=& \mathbf{9437184} \\ \hline \end{array}\)

 

There are 20 terms in the sequence.

 

laugh

 May 4, 2021
edited by heureka  May 4, 2021

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