Answer:
[tex]\bold{a_n = 24\left(-\frac32\right)^{n-1}}[/tex]
Step-by-step explanation:
[tex]a_1=24\\a_2=-36\\a_3=54\\\\\dfrac{a_2}{a_1}=\dfrac{-36}{24}=-\dfrac32\\\\ \dfrac{a_3}{a_2}=\dfrac{54}{-36}=-\dfrac32\\\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=-\dfrac32[/tex]
So, this is geometric sequence with common ratio: r = -³/₂
Therefore the formula:
[tex]a_n=a_1\cdot q^{n-1}\\\\a_n = 24\left(-\frac32\right)^{n-1}[/tex]
