Question

What is the missing term in the geometric sequence?

-6,24,?,384,-1536,...
A) -204
B) -144
C) -96

Answer 1

is a geometric sequence, so that means a number is multiplying to current term to get the next one... meaning if we simply divide those two terms, the quotient is that "multiplier", namely the "common ratio"

so... hmm let's try say -1536 and 384


`\bf \cfrac{-1536}{384}\implies -4\impliedby \textit{common ratio} \\\\\\ n^(th)\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^(n-1)\qquad \begin{cases} a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ n=n^(th)\ term\\ ----------\\ a_1=-6\\ r=-4\\ n=3 \end{cases} \\\\\\ \textit{the third term is then }\implies a_3=(-6)(-4)^(3-1) \\\\\\ a_2=(-6)(-4)^2\implies a_2=-6\cdot 16\implies a_2=-96`