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Find a formula for the general term $ a_n $ of the sequence, assuming that the pattern of the first few terms continues.$ \left\{ -3, 2, - \frac {4}{3}, {8}{9}, - \frac {16}{27}, . . .\right\} $

$-3\left(-\frac{2}{3}\right)^{n-1}$

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 1

Sequences

Series

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Let's find a formula for the general term of this sequence. So we see that we're starting off with three. Then how are we getting to two? Are we getting there by adding, or by multiplying? Well, if we didn't get there by adding would have to add five. But if we add five to two, we'd get to seven. Not negative for over three. So perhaps this is a she measured sequence, and here were multiplying. Bye. Negative. Two over three. So if we start off with three negative three multiplied by negative to over three, you get to two times negative to over three negative for over three, which is over here and so on. So it looks like we take to find a n. You start off with the first term, and then you multiply by negative to over three and minus one times. So this is the formula for the end of term of the sequence, and that's our final answer.

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