Question
Find the 10 th term of the geometric sequence
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In this geometric sequence, the first term is 9 and the common ratio can be found by dividing the second term by the first term: . The formula for the -th term of a geometric sequence is given by . Plugging in the values for the 10th term:

The 10th term is .

But, what’s a geometric sequence without a little bit of flair? These sequences are like a rollercoaster, where each twist and turn keeps multiplying the thrill! You start off at one height (the first term), and with each loop (the common ratio), the excitement either skyrockets or spirals downward—like our negative ratio making the terms flip between positive and negative!

If you’re curious about how geometric sequences pop up in various fields, consider finance! They’re often used in calculating compound interest, where your initial investment multiplies by a set ratio each period. Who knew that investing could feel like riding that rollercoaster of numbers? It’s all about knowing when to hold on tight or let go!