The second most common kind of sequence is the geometric sequence. A good idea is to compare and contrast the steps in computing arithmetic and geometric sequences. Then, like we did with arithmetic sequences, make a plot of the sequence using (n, An). What sort of function does this sequence look like and how does that validate the formula for the general term in a geometric sequence? Consider plotting on Desmos and sharing your graph!
In geometric sequnce the common ratio between the two consecutive terms remain constant, so if a be the first term of the sequece and r be the common ratio, then we have
Multiplying the above ratio, we get
which gives the nth term of the geometric sequence.
Consider the geometric sequence
the graph of this sequnce is shown in figure below:
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