Chapter 11 - Section 11.2 - Arithmetic and Geometric Sequences - Exercise Set: 6

$-2,-4,-8,-16,-32$

Work Step by Step

The general term $a_n$ of a geometric sequence is given by $a_n = a_1r^{n-1}$ where $a_1$ is the first term and $r$ is the common ratio. We plug in $n = 1, 2, 3, 4, 5$ to find the first five terms of the geometric sequence $a_1 = -2\cdot2^{1-1} = -2\cdot2^0=-2\cdot1=-2$ $a_2 = -2\cdot2^{2-1} = -2\cdot2^1=-2\cdot2=-4$ $a_3 = -2\cdot2^{3-1} = -2\cdot2^2=-2\cdot4=-8$ $a_4 = -2\cdot2^{4-1} = -2\cdot2^3=-2\cdot8=-16$ $a_5 = -2\cdot2^{5-1} = -2\cdot2^4=-2\cdot16=-32$

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