what is the next term in the geometric sequence 4,-12,36
Answer (2)
Answer:4,-12,36,-108Step-by-step explanation:4(-3),-12(-3),36(-3),-108
SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & n = 4 \\ & a_1 = 4 \\ & a_2 = -12 \\ & a_3 = 36 \end{aligned}[/tex]Step 2: Find the common ratio.[tex]\begin{aligned} r & = \frac{a_2}{a_1} = \frac{a_3}{a_2} \\ r & = \frac{-12}{4} = \frac{36}{-12} \\ r & = -3 = -3 \end{aligned}[/tex]Step 3: Solve for the next term (4th term) of a geometric sequence.[tex]\begin{aligned} a_n & = a_1r^{n - 1} \\ a_4 & = (4)(-3)^{4 - 1} \\ & = 4(-3)^3 \\ & = 4(-27) \\ & = \boxed{-108} \end{aligned}[/tex]Hence, the next term is -108.
