Question

Which type of sequence is represented by the given table?

Answer 1

Answer:

A.  

The table represents a geometric sequence because the successive y-values have a common ratio of -2.4.

Step-by-step explanation:

A geometric sequence, with a first term a and common ratio r, is generally represented as;

$a,ar,ar^{2},ar^{3},ar^{4},............ar^{n}$

The first term refers to the first number that appears in the sequence. The common ratio is the constant that multiplies a preceding value to obtain the successive one. That is, to obtain $ar^{2}$ from $ar$ we multiply $ar$ by the common ratio r.

In the table given the y-values are as follows;

4, -9.6, 23.04, -55.296

To obtain the common ratio we simply divide each value by the preceding one;

(-9.6)/4 = -2.4

23.04/(-9.6) = -2.4

(-55.296)/23.04 = -2.4

Since the sequence of numbers has a common ratio then it qualifies to be a geometric sequence. Thus, the table represents a geometric sequence because the successive y-values have a common ratio of -2.4.