Find from a geometric sequence where the first
term is -5 and r is 3 .
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To find in a geometric sequence, we can use the formula for the -th term, which is given by . Here, and . Plugging in these values for :

Calculating , we get:

So, .

If you ever find yourself confused about geometric sequences, just remember that the first term sets the stage, while the common ratio is your spotlight—amplifying each term like a dramatic performance! Each term is a multiplication of the previous one, making it a thrilling ride through numbers!

For practical uses, geometric sequences pop up everywhere—from calculating compound interest in finance to predicting population growth! Whenever you encounter situations involving exponential changes, think of a geometric sequence dancing its way through—they’re like the “rock stars” of math, effortlessly multiplying their way to success!