Problem Solving

In a geometric sequence, each term is a constant multiple of the preceding one. if the first three terms in a geometric sequence are -2, x and -8 which of the following could be the sixth term in the series.
a. -4096
b. -32
c. 32
d. 1024
e. 2048

Confused between b and c... Please enlighten

Seems to be a problem with the answer choices.

Let the constant be y

therefore, x = -2y and -8 = xy. Solving for y, we get y = 2 or -2.

Hence sixth tersm = -8 multiply (2x2x2) or -8 multiply (-2x-2x-2)
From this, the sixth term can be either 64 or -64. None of the answer choices show this.

nirjagrl wrote:In a geometric sequence, each term is a constant multiple of the preceding one. if the first three terms in a geometric sequence are -2, x and -8 which of the following could be the sixth term in the series.
a. -4096
b. -32
c. 32
d. 1024
e. 2048

Confused between b and c... Please enlighten

As shown by Gaurav, the question has 2 problems:
1. The common factor can be calculated to either 2 or -2. With 2 as the common factor the first 3 terms of the series would be -2, -4, -8... whereas with -2 as the common factor the first 3 terms of the series would be -2, 4, -8... With either of the common factor it adheres to -2, x, -8
2. With the common factor problem, the solution of the sixth term should be either 64 or -64. (-2, 4, -8, 16, -32, 64 OR -2, -4, -8, -16, -32, -64). Since neither 64, nor -64 are in the list of options, the question cannot be answered

Regards,
Aparna Aggarwal

Suppose the first term is a, and we multiply each term by b to get the following term. That means our sequence is

a, a*b, a*b*b, a*b*b*b, ...

We know a = -2, and we know a*b*b = -8, so b*b = 4, and b = -2 or b = 2.

The sixth term will be a*b*b*b*b*b, so it's either -2*32 or -2*(-32).

This seems to come from a GMAT book I've never heard of, and the answer choices there do contain one correct option (64).