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What is the 4th term of the sequence defined by a_n = n^2 + 2n? (2023)

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Question: What is the 4th term of the sequence defined by a_n = n^2 + 2n? (2023)

Options:

  1. 24
  2. 30
  3. 36
  4. 42

Correct Answer: 24

Exam Year: 2023

Solution: 

For n = 4, a_4 = 4^2 + 2*4 = 16 + 8 = 24.

What is the 4th term of the sequence defined by a_n = n^2 + 2n? (2023)

Practice Questions

Q1
What is the 4th term of the sequence defined by a_n = n^2 + 2n? (2023)
  1. 24
  2. 30
  3. 36
  4. 42

Questions & Step-by-Step Solutions

What is the 4th term of the sequence defined by a_n = n^2 + 2n? (2023)
  • Step 1: Identify the formula for the sequence, which is a_n = n^2 + 2n.
  • Step 2: Determine the value of n for the 4th term, which is n = 4.
  • Step 3: Substitute n = 4 into the formula: a_4 = 4^2 + 2*4.
  • Step 4: Calculate 4^2, which is 16.
  • Step 5: Calculate 2*4, which is 8.
  • Step 6: Add the results from Step 4 and Step 5: 16 + 8 = 24.
  • Step 7: Conclude that the 4th term of the sequence is 24.
  • Quadratic Sequences – Understanding how to evaluate a quadratic expression for a given integer value.
  • Substitution – Correctly substituting the value of n into the formula to find the term in the sequence.
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