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Verdich [7]
3 years ago
15

Find the pattern and use it to list the nth term in the sequence. 3, 9, 27, 81, 243 ...

Mathematics
1 answer:
KonstantinChe [14]3 years ago
3 0

The pattern is formed a geometric sequence

The nth term of the sequence is a_{n}=3^{n}

Step-by-step explanation:

The formula of the nth term of a geometric sequence is:

a_{n}=ar^{n-1} , where

  • a is the first term
  • r is the common ratio between the consecutive terms

∵ The pattern is 3 , 9 , 27 , 81 , 243

∵ 9 ÷ 3 = 3

∵ 27 ÷ 9 = 3

∵ 81 ÷ 27 = 3

∵ 243 ÷ 81 = 3

- There is a common ratio 3 between each two consecutive terms

∴ The pattern is formed a geometric sequence

∵ The first term is 3

∴ a = 3

∵ The common ratio is 3

∴ r = 3

- To find the nth term substitute a and r in the formula above

∵ a_{n}=ar^{n-1}

∴ a_{n}=3(3)^{n-1}

- Remember we add the powers of the same base with multiplication

∵ 3 × 3^{n-1} = 3^{1+n-1}

∴ 3 × 3^{n-1} = 3^{n}

∴ a_{n}=3^{n}

∴ The nth term of the sequence is  a_{n}=3^{n}

Learn more:

You can learn more about the sequences in brainly.com/question/1522572

#LearnwithBrainly

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2 years ago
4.3 Mr Mokwebo 's two sons, Refentse and Tokelo have just passed grade 7 and grade 9 respectively. He will give them some money
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The amount of money each of Mr Mokwebo 's two sons; Tokelo and Refentse will get is R116 and R95 respectively.

<h3>How to write and solve equation:</h3>

  • Amount needed to buy chocolate = R253
  • Tokelo's money = x
  • Refentse's money = x - 21

Total amount needed = Tokelo's money + Refentse's money

253 = x + (x - 21)

253 = x + x - 21

253 = 2x - 21

253 - 21 = 2x

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1 year ago
A skateboard ramp has a slope of 4/9. What is the measure of the angle the ramp forms with the ground
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7 0
3 years ago
find an equation for the perpendicular bisector of the line segment whose endpoints are (-8,-5) and (-4,1)
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Answer:

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Step-by-step explanation:

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so midpoint is (-6,-2)

Slope of the line: Slope m = (y2-y1)/(x2-x1)

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Perpendicular lines have slopes that are negative reciprocals of one another

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Using (-6,-2)

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6 0
2 years ago
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