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nignag [31]
2 years ago
5

Which formula can be used to describe the sequence? -2/3,-4,-24,-144...

Mathematics
1 answer:
koban [17]2 years ago
8 0

The formula can be used to describe the sequence is a_{n}=\frac{-2}{3}(6)^{n-1}

Step-by-step explanation:

The formula of the nth term of the geometric sequence is a_{n}=a(r)^{n-1} , where

  • a is the first term of the sequence
  • r is the common ratio between each two consecutive terms
  • r=\frac{a_{2}}{a_{1}} = \frac{a_{3}}{a_{2}}

∵ The sequence is \frac{-2}{3} , -4 , -24 , -144 , .......

∵ The 1st term is \frac{-2}{3}

∵ The 2nd term is -4

∴ \frac{-4}{\frac{-2}{3}}=6

∵ The 3rd term is -24

∴ \frac{-24}{-4}=6

∵ The 4th term is -144

∴ \frac{-144}{-24}=6

∵  \frac{a_{2}}{a_{1}} = \frac{a_{3}}{a_{2}} =  \frac{a_{4}}{a_{3}} = 6

∴ There is a constant ratio between each two consecutive terms

∴ The sequence is a geometric sequence

∵ The formula of the nth term of the geometric sequence is a_{n}=a(r)^{n-1}

∵ a = \frac{-2}{3}

∵ r = 6

∴ The formula of the sequence is a_{n}=\frac{-2}{3}(6)^{n-1}

The formula can be used to describe the sequence is a_{n}=\frac{-2}{3}(6)^{n-1}

Learn more:

You can learn more about sequences in brainly.com/question/7221312

#LearnwithBrainly

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