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strojnjashka [21]
2 years ago
5

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

ce. If geometric, state the common ratio.
-4, 12, -36, 108, -324, …
My answer below?
12, - 4 = 8
4 -12= -8 (neither)
Mathematics
2 answers:
WARRIOR [948]2 years ago
7 0

Answer:

okay

Step-by-step 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  \div ( - 4) =  - 3 \\ r = ( - 36) \div 12 =  - 3 \\ r = 108 \div ( - 36) =  - 3 \\ since \: r \: is \: the \: same \: this \: is \: a \: geometric \: serie

PilotLPTM [1.2K]2 years ago
3 0

\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{ \dfrac{12}{-4} = -3}

  • \sf{ \dfrac{-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}

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