Question
For the following sequences, plot the first 25 terms of the sequence and state whether the graphical evidence suggests that the sequence converges or diverges.$$a_{n}=\sin n$$
Step 1
The nth term of the sequence is given by the formula $a_{n}=\sin n$. So, we substitute the values of n from 1 to 25 into the formula to get the first 25 terms. Show more…
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For the following sequences, plot the first 25 terms of the sequence and state whether the graphical evidence suggests that the sequence converges or diverges. $$a_{n}=\cos n$$
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Plot the first $N$ terms of each sequence. State whether the graphical evidence suggests that the sequence converges or diverges. $ a_{1}=1, \quad a_{2}=2, \quad$ and $\quad$ for $\quad n \geq 2,$ $a_{n}=\frac{1}{2}\left(a_{n-1}+a_{n-2}\right) ; \quad N=30$
Plot the first $N$ terms of each sequence. State whether the graphical evidence suggests that the sequence converges or diverges. $a_{1}=1, \quad a_{2}=2, \quad$ and $\quad$ for $\quad n \geq 3,$ $a_{n}=\sqrt{a_{n-1} a_{n-2}} ; \quad N=30$
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