Question

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

Answer 1

a₁₃ = 1 464 843 750

Explanation:

`a_1=6\\a_2=-30\\a_3=150\\\\(a_2)/(a_1)=(-30)/(6)=-5\quad\wedge\quad (a_2)/(a_2)=(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`