Question

Which of the following best describes the following set of numbers?

2, -2, 2, -2, ...
Finite arithmetic sequence
Infinite geometric sequence
Finite geometric sequence
Infinite arithmetic sequence

Answer 1

2, -2, 2, -2, ...

This is a geometric progression.

First term = 2

The rate of geometric progression = -1

a1 = 2

a2 = a1 × (-1) = -2

a3 = a2 × (-1) = 2

And so on

⇒ This is a infinite geometric sequence

Answer 2

Infinite geometric sequence

Explanation:

2, -2, 2, -2, ...

Lets find the difference of the terms

-2 -2=0

2-(-2)=0

LEts check with common ratio

-2/2= -1

2/-2=-1

so common ratio r=0, so its geometric

The sequence is repeating because of common ratio -1

So it goes on infinitely

Hence it is Infinite geometric sequence