Which one of the following is a geometric sequence?

Question

A. 2, -3, 9/2, -18/4
B. 0, 1, 2, 3,...
C. 8, 4, 2, 1, 1/2, 1/4,...
D -7, 10, 23, 36,...

Answer 1

C

Answer 2

The answer is C:
4 = 8 * 1/2
2 = 4 * 1/2
1 = 2 * 1/2
1/2 = 1 * 1/2
1/4 = 1/2 * 1/2

Geometric implies multiplication. The multiplying factor from one term to the next in this example is 1/2.

Answer B would be an arithmatic progressive where the factor is adding 1 to the previous term.

Answer A has a geometric factor of -3/2 for the first three terms -- 2 * -3/2= -3; -3*-3/2 = 9/2 -- but the final term is 9/2 * -1.

Answer D has a arithmatic factor of +13 for the final three terms, but the first and second terms are connected by a factor of +17.

Answer 3

A. 2, -3, 9/2, -18/4 is a geometric sequence, cos if u divide -18/4 by the next term before it, and so foth and so on, the denominator common that is -1/2

Answer 4

A is multiplying a term times in a varying pattern.
2*-1.5 = -3
-3*-1.5 = 9/2
(9/2)*-1.0 = (-9/2) or (-18/4)
So the absolute value of number it's getting multiplied with, decreases for every other two. So it's not consistent and thus not geometric.
B is simply adding one to the previous term and not getting multiplied by anything and thus not geometric.
D is just random as far as I can see. But it's surely not getting multiplied with anything consistently. So it's not geometric.
C is geometric because the next term in the sequence made by the previous term getting multiplied with 1/2.

Answer 5

this is how to find a GP

say the terms are a b c d
then

a/b =b/c =c/d

so

A and C part are geometric series as

2/-3 = -3/ (9/2)....

and

8/4 = 4/2 = 2/1 ...

so ans is A and C

Answer 6

Careful Doug, 9/2 * -3/2 does not equal -18/4 ;)

Answer 7

In a geometric sequence, each term is a multiple of the previous term. So both (a) and (c) are geometric sequences.

In (c) each term is the previous term times 1/2.
In (a) each term is the previous term times -3/2.


Doug

Answer 8

ANS : C

an = a1 * r^(n - 1)

or in this case

an = a1 * r^(-(n - 1)
or
an = (a1)/(r^(n - 1))

a(1) = 8/(2^(1 - 1))
a(1) = 8/(2^0)
a(1) = 8/1
a(1) = 8

a(2) = 8/(2^(2 - 1))
a(2) = 8/(2^1)
a(2) = 8/2
a(2) = 4

a(3) = 8/(2^(3 - 1))
a(3) = 8/(2^2)
a(3) = 8/4
a(3) = 2

a(4) = 8/(2^(4 - 1))
a(4) = 8/(2^3)
a(4) = 8/8
a(4) = 1

a(5) = 8/(2^(5 - 1))
a(5) = 8/(2^4)
a(5) = 8/16
a(5) = 1/2

a(6) = 8/(2^(6 - 1))
a(6) = 8/(2^5)
a(6) = 8/32
a(6) = 1/4

Answer 9

C
A geometric progression is a sequence of numbers such as a(k)/a(0)=r^(-k) k=0,1,2,3,.. r-constant ratio term

In your case it is 8, 4, 2, 1, 1/2, 1/4,... a(k)=a(0)r^(-k) k=0,1,2,3,.. Where r=2

Answer 10

C,
Because Second term divided by first term is 1/2
Because Third term divided by second term is 1/2
Because fourth term divided by third term is 1/2
Because fifth term divided by fourth term is 1/2
Since the common ratio is same i.e. 1/2 therefore this series is in geometric series

Answer 11

c