Question

Find the next two terms of each geometric sequence (show work)

Answer 1

Answer:

$\huge\boxed{1.\ -120,\ -240}\\\boxed{2.\ \dfrac{10}{3},\ \dfrac{10}{9}}\\\boxed{3.\ \dfrac{27}{32},\ \dfrac{81}{64}}$

Step-by-step explanation:

$\text{if}\\a_1,\ a_2,\ a_3,\ ...\text{is a geometric sequence}\\\text{then}\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...=\dfrac{a_n}{a_{n-1}}=const.=r\\\\a_n=a_{n-1}r$

$1.\\-15,\ -30,\ -6\\\\\dfrac{-30}{-15}=-2;\ \dfrac{-6}{-30}=\dfrac{1}{5}$

it,s not a geometric sequence...

I think it should be:

$-15,\ -30,\ -60,\ ...\\\\\dfrac{-30}{-15}=2;\ \dfrac{-60}{-30}=2\\\\next\\\\-60\cdot2=-120\\-120\cdot2=-240$

$2.\\90,\ 30,\ 10,\ ...\\\\\dfrac{30}{90}=\dfrac{1}{3};\ \dfrac{10}{30}=\dfrac{1}{3}\\\\next\\\\10\cdot\dfrac{1}{3}=\dfrac{10}{3}\\\\\dfrac{10}{3}\cdot\dfrac{1}{3}=\dfrac{10}{9}$

$3.\\\dfrac{1}{4},\ \dfrac{3}{8},\ \dfrac{9}{16},\ ...\\\\\dfrac{\frac{3}{8}}{\frac{1}{4}}=\dfrac{3}{8}\cdot\dfrac{4}{1}=\dfrac{3}{2};\ \dfrac{\frac{9}{16}}{\frac{3}{8}}=\dfrac{9}{16}\cdot\dfrac{8}{3}=\dfrac{3}{2}\\\\next\\\\\dfrac{9}{16}\cdot\dfrac{3}{2}=\dfrac{27}{32}\\\\\dfrac{27}{32}\cdot\dfrac{3}{2}=\dfrac{81}{64}$