Question

which of these is a geometric sequence a)2,3,5,9,17.... b)3,6,9,12.... c) 4,2,1,1/2,1/4.... d)3,-15,-33,-51,-69....

Answer 1

c is the geometric sequence

Answer 2

The required option is C) $4,2,1,\dfrac{1}{2},\dfrac{1}{4} ,....$.

Step-by-step explanation:

Common ratio(r)$\dfrac{second term}{First term} =\dfrac{Third term}{second term}$, are equal the sequence in geometric sequence.

Check options:

a) 2, 3, 5, 9, 17....

Common ratio(r) $=\dfrac{3}{2}$ or $\dfrac{5}{3}$

$\dfrac{3}{2} \neq \dfrac{5}{3}$, the sequence is not geometric sequence.

b) 3, 6, 9, 12....

Common ratio(r) $=\dfrac{6}{3}=2$ or, $\dfrac{9}{6}=\dfrac{3}{2}$

$2\neq \dfrac{3}{2}$, the sequence is not geometric sequence.

c) $4,2,1,\dfrac{1}{2},\dfrac{1}{4} ,...$

Common ratio(r) $=\dfrac{2}{4}=\dfrac{1}{2}$or, $\dfrac{1}{2}$

$\dfrac{1}{2}=\dfrac{1}{2}$, the sequence is geometric sequence.

d) 3,-15, -33, -51, -69....

Common ratio(r) $=\dfrac{-15}{3}=-5$ or, $\dfrac{-33}{-15}=\dfrac{11}{5}$

$-5\neq \dfrac{11}{5}$, the sequence is not geometric sequence.

Hence, the required option is C) $4,2,1,\dfrac{1}{2},\dfrac{1}{4} ,...$.