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What is the 6th term of the sequence defined by a_n = n^2 - n + 1? (2023)

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Question: What is the 6th term of the sequence defined by a_n = n^2 - n + 1? (2023)

Options:

  1. 31
  2. 35
  3. 36
  4. 30

Correct Answer: 36

Exam Year: 2023

Solution: 

Substituting n = 6 gives a_6 = 6^2 - 6 + 1 = 36 - 6 + 1 = 31.

What is the 6th term of the sequence defined by a_n = n^2 - n + 1? (2023)

Practice Questions

Q1
What is the 6th term of the sequence defined by a_n = n^2 - n + 1? (2023)
  1. 31
  2. 35
  3. 36
  4. 30

Questions & Step-by-Step Solutions

What is the 6th term of the sequence defined by a_n = n^2 - n + 1? (2023)
  • Step 1: Identify the formula for the sequence, which is a_n = n^2 - n + 1.
  • Step 2: Determine the value of n for the 6th term, which is n = 6.
  • Step 3: Substitute n = 6 into the formula: a_6 = 6^2 - 6 + 1.
  • Step 4: Calculate 6^2, which is 36.
  • Step 5: Subtract 6 from 36: 36 - 6 = 30.
  • Step 6: Add 1 to 30: 30 + 1 = 31.
  • Step 7: Conclude that the 6th term of the sequence is 31.
  • Sequence Evaluation – The question tests the ability to evaluate a mathematical sequence using a given formula.
  • Substitution – The question requires substituting a specific value into the formula to find the corresponding term.
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