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.
+26367 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.
