Math  /  Algebra

QuestionThe third and fourth terms of an arithmetic sequence are the first and second terms of a geometric sequence. If the first two terms of the arithmetic sequence are 5,2 , then what is the fourth term of the geometric sequence?

Studdy Solution
Calculate the fourth term of the geometric sequence.
The third term of the geometric sequence g3 g_3 is:
g3=g1r2=(1)42=116=16 g_3 = g_1 \cdot r^2 = (-1) \cdot 4^2 = -1 \cdot 16 = -16
The fourth term of the geometric sequence g4 g_4 is:
g4=g3r=164=64 g_4 = g_3 \cdot r = -16 \cdot 4 = -64
The fourth term of the geometric sequence is:
64 \boxed{-64}

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