Calculate the 8th Term in the Sequence: Applying the Rule 2(2n-2)

A sequence has a term-to-term rule of 2(2n−2) 2(2n-2) .

What is the 8th element of the sequence?

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Step-by-step video solution

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00:00 Find the 8th element in the sequence
00:03 The desired element's position according to the given data
00:07 We'll substitute the appropriate position in the formula and solve to find the element
00:11 Always solve parentheses first
00:14 Always solve multiplication and division before addition and subtraction
00:26 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

A sequence has a term-to-term rule of 2(2n−2) 2(2n-2) .

What is the 8th element of the sequence?

2

Step-by-step solution

To find the 8th element of the sequence, we follow these steps:

  • Substitute n=8 n = 8 into the given sequence formula an=2(2n−2) a_n = 2(2n-2) .
  • Calculate a8=2×(2×8−2) a_8 = 2 \times (2 \times 8 - 2) .
  • Simplify inside the parentheses: 2×8−2=16−2=14 2 \times 8 - 2 = 16 - 2 = 14 .
  • Now compute a8=2×14=28 a_8 = 2 \times 14 = 28 .

Therefore, the 8th element of the sequence is 28 28 .

3

Final Answer

28 28

Practice Quiz

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Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

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