Week 2 – Geometric Series

This week in Pre-Calc 11 we learned how to work with Geometric Sequences and Geometric Series. A Geometric Sequence is a sequence of numbers that is multiplied by a common ratio each term. For example, -3, 6, -12, 24 is an example of an arithmetic sequence with a common ratio of  -2. -3 x 2 = 6 and 6 x -2 = -12

In order to find the unknown term of an Arithmetic Sequence you would use the formula t_n = a \times (r) ^n-1 (the minus one relating to the “n” in this formula, I was unable to figure out the coding for this section)

if we use this formula and plug in the numbers from my example sequence, we can find whatever term we want as long as we know the “Common Ratio” and the first term (a)

If we were to determine the 7th term of this sequence we would use t_7 = -3 \times(-2)^6 giving us the answer = 192

 

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