Question

Determine whether each of the following sequences are arithmetic, geometric or neither. If arithmetic, state the common difference. If geometric, state the common ratio.

-4, 12, -36, 108, -324, …
My answer below?
12, - 4 = 8
4 -12= -8 (neither)

Answer 1

okay

Explanation:

`for arithmetic \: progression \: there \: must \: be \: a \: common \: difference \\ \\ to \: get \: common \: difference \: {d} \: \\ get \: the \: the \: term \: infront \: minus \: the \: term \: before \\ say \: d = 12 - ( - 4) = 16 \\ d = - 36 - 12 = - 48 \\ d = 108 - ( - 36) = 144 \\ since \: d \: isnt \: uniform \: this \: is \: not \: arithmetic \: progression \\ \\ for \: geometric \: progression \: there \: must \: be \: a \: common \: ratio \: {r} \\ r \: is \: got \: by \: dividing \: the \: term \: infront \: by \: the \: term \: behind \\ \\ say \: r = 12 / ( - 4) = - 3 \\ r = ( - 36) / 12 = - 3 \\ r = 108 / ( - 36) = - 3 \\ since \: r \: is \: the \: same \: this \: is \: a \: geometric \: serie`

Answer 2

`\qquad\qquad\huge\underline{{\sf Answer}}`

`\textbf{Let's see if the sequence is Arithmetic or Geometric :}`

`\textsf{If the ratio between successive terms is }`
`\textsf{equal then, the terms are in GP}`

• 
  `\sf{ (12)/(-4) = -3}`

• 
  `\sf{ (-36)/(12) = -3}`

`\textsf{Since the common ratio is same, }`
`\textsf{we can infer that it's a geometric progression}`
`\textsf{with common ratio of -3}`