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In a sequence defined by a_n = n^2 + n, what is the value of a_5? (2023)

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Question: In a sequence defined by a_n = n^2 + n, what is the value of a_5? (2023)

Options:

  1. 30
  2. 25
  3. 20
  4. 15

Correct Answer: 30

Exam Year: 2023

Solution: 

Substituting n = 5 gives a_5 = 5^2 + 5 = 25 + 5 = 30.

In a sequence defined by a_n = n^2 + n, what is the value of a_5? (2023)

Practice Questions

Q1
In a sequence defined by a_n = n^2 + n, what is the value of a_5? (2023)
  1. 30
  2. 25
  3. 20
  4. 15

Questions & Step-by-Step Solutions

In a sequence defined by a_n = n^2 + n, what is the value of a_5? (2023)
  • Step 1: Identify the formula for the sequence, which is a_n = n^2 + n.
  • Step 2: Determine the value of n we want to use. In this case, n = 5.
  • Step 3: Substitute n = 5 into the formula: a_5 = 5^2 + 5.
  • Step 4: Calculate 5^2, which is 25.
  • Step 5: Add 5 to 25: 25 + 5 = 30.
  • Step 6: Conclude that the value of a_5 is 30.
  • Sequence Evaluation – Understanding how to evaluate a sequence defined by a formula.
  • Substitution – Correctly substituting a value into a mathematical expression.
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