What is the common ratio of the geometric sequence below? –96, 48, –24, 12, –6, a, -2 b,-1/2 c, 2 d, 1/2

Option b is correct.

The common ratio for the given geometric sequence is;

Step-by-step explanation:

The given sequence is;  -96, 48 , -24, 12 , -6, .....

Since, given sequence is Geometric

Geometric Sequence in which each term is found by multiplying the previous term by a constant(i.e common ratio)

In general we write geometric sequence as;

where a be the first term and r is the common ratio.

On comparing the given sequence with general geometric sequence;

we get

a = -96                  ......[1]

ar = 48                   ......[2]

ar^2 = -24              .....[3]

and so on....        

To find the common ratio i.e, r;

Divide equation [2] by [1];

Simplify:

Similarly,

by dividing the equation [3] by [2] we get;

Simplify:

As, you can see that the value of r is constant i.e, in the given sequence.

Therefore, the common ratio for the given geometric sequence is;

The common ratio of the geometric sequence is

Further Explanation:

If the first term a and the second term ar is known then, the value of r can be obtained as follows,

The nth term of the geometric sequence can be obtained as,

Given:

The geometric sequence is

The options are as follows,

(a).

(b).

(c).

(d).

Explanation:

The first term of the geometric sequence is , second term of the geometric sequence is 48, third term , the fourth geometric sequence is 12 and the fifth term of the sequence is

The common ratio r between the second and first term can be obtained as follows.

The common ratio between the second and third term can be obtained as follows.

The common ratio of the geometric sequence is

Option (a) is not correct.

Option (b) is correct.

Option (c) is not correct.

Option (d) is not correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Geometric progression

Keywords: geometric sequence, fraction, written as, common ratio, first term, second term, sum of geometric sequence, 768, 480, 300, 187.5.

step-by-step explanation: