Question

The first four terms of a sequence are shown on the graph below. On a coordinate plane, points are at (1, negative 1), (2, 8), (3, negative 16), (4, 32). What can be concluded about the sequence? The common ratio of the sequence is 2. The common difference of the sequence is 2. The next term of the sequence is represented by the point (5, 64). The next term of the sequence is represented by the point (5, –64).

Answer 1

• The next term of the sequence is represented by the point (5, –64)

Explanation:

Note: The first point should be (1, - 4)

According to the points, the sequence is:

• t₁ = - 4, t₂ = 8, t₃ = - 16, t₄ = 32

or

• - 4, 8, - 16, 32, ...

We can observe it is a geometric sequence with common ratio of - 2, as:

• r = 32/ - 16 = - 16/8 = 8/ - 4 = - 2

The following term is:

• t₅ = t₄*r = 32*(- 2) = - 64

The coordinates of same term are:

• (5, - 64)

As we see the correct answer choice is D.