Question

Determine whether the following sequence is geometric. If so, find the common ratio,

Answer 1

Answer:

Yes, the sequence is geometric

common ratio (r) = -3

Step-by-step explanation:

Given:

• $a_1=1$
• $a_2=-3$
• $a_3=9$
• $a_4=-27$

If a sequence is geometric, common ratio $r$:

$r=\dfrac{a_4}{a_3}=\dfrac{a_3}{a_2}=\dfrac{a_2}{a_1}$

Substituting the given values:

$\implies \dfrac{a_4}{a_3}=\dfrac{-27}{9}=-3$

$\implies \dfrac{a_3}{a_2}=\dfrac{9}{-3}=-3$

$\implies \dfrac{a_2}{a_1}=\dfrac{-3}{1}=-3$

Therefore, as

$\dfrac{a_4}{a_3}=\dfrac{a_3}{a_2}=\dfrac{a_2}{a_1}=-3$

the sequence is geometric with common ratio of -3