Question

Find the 13th term of the geometric sequence 6, -30,150

Answer 1

Answer:

            a₁₃ = 1 464 843 750

Step-by-step explanation:

$a_1=6\\a_2=-30\\a_3=150\\\\\dfrac{a_2}{a_1}=\dfrac{-30}{6}=-5\quad\wedge\quad \dfrac{a_2}{a_2}=\dfrac{150}{-30}=-5\quad\implies\ \ q=-5\\\\\\a_n=a_1\cdot q^{n-1}\\\\a_{13}=a_1\cdot q^{12}=6\cdot(-5)^{12}=6\cdot244140625=1464843750$