Question

How do you tell whether the sequence `0, -5, -10, -12, -20` is arithmetic?

Answer 1

Since the difference between the successive terms is not uniformly equal,`color(red)(" it is not an Arithmetic Sequence"`

Explanation:

Given `a_1 = 0, a_2 = -5, a_3 = -10, a_4 = -12, a_5 = -20`

`a_2 - a_1 = -5 - 0 =color(red)( -5`

`a_3 - a_2 = - 10 - (-5) = color(red)(-5`

`a_4 - a_3 = -12 - (-10) =color(red)( -2`

`a_5 - a_4 = -20 - (-12) = color(red)(-8`

Since the difference between the successive terms is not uniformly equal,`color(red)(" it is not an Arithmetic Sequence"`