Find the Variable Expression for Sequence: 3, 8.5, 14, 19.5, 25

Given the series whose difference between two jumped numbers is constant:

3,8.5,14,19.5,25 3,8.5,14,19.5,25

Describe the property using the variable n n

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the sequence formula
00:04 This is the first term according to the given data
00:08 Let's observe the change between terms (D) according to the given data
00:29 We'll use the formula to describe the sequence
00:37 We'll substitute appropriate values and solve to find the sequence formula
00:51 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Given the series whose difference between two jumped numbers is constant:

3,8.5,14,19.5,25 3,8.5,14,19.5,25

Describe the property using the variable n n

2

Step-by-step solution

To solve this problem, let's derive the formula for the arithmetic sequence:

  • Step 1: Identify the first term a1a_1. In this series, the first term is 33.
  • Step 2: Determine the common difference dd. By calculation, the difference between each consecutive term is constant at 5.55.5.
  • Step 3: Use the common formula for an arithmetic sequence: a(n)=a1+(n1)da(n) = a_1 + (n-1) \cdot d.
  • Step 4: Substitute the values into the formula: a(n)=3+(n1)5.5a(n) = 3 + (n-1) \cdot 5.5.

Applying these steps confirms the general term for this arithmetic sequence is:

a(n)=3+(n1)×5.5 a(n) = 3 + (n-1) \times 5.5

Thus, the correct formulation for n n -th term of the sequence is given by this expression.

Therefore, the correct answer is choice 3: a(n)=3+(n1)×5.5 a(n)=3+(n-1)\times5.5 .

3

Final Answer

a(n)=3+(n1)×5.5 a(n)=3+(n-1)\times5.5

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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