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If the nth term of a sequence is given by a_n = n^2 + n, what is a_4?

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Question: If the nth term of a sequence is given by a_n = n^2 + n, what is a_4?

Options:

  1. 20
  2. 24
  3. 16
  4. 18

Correct Answer: 20

Solution: 

a_4 = 4^2 + 4 = 16 + 4 = 20.

If the nth term of a sequence is given by a_n = n^2 + n, what is a_4?

Practice Questions

Q1
If the nth term of a sequence is given by a_n = n^2 + n, what is a_4?
  1. 20
  2. 24
  3. 16
  4. 18

Questions & Step-by-Step Solutions

If the nth term of a sequence is given by a_n = n^2 + n, what is a_4?
  • Step 1: Identify the formula for the nth term of the sequence, which is a_n = n^2 + n.
  • Step 2: Substitute n with 4 in the formula to find a_4. So, we calculate a_4 = 4^2 + 4.
  • Step 3: Calculate 4^2, which is 16.
  • Step 4: Add 4 to the result from Step 3. So, 16 + 4 = 20.
  • Step 5: Conclude that a_4 = 20.
  • Sequence Evaluation – Understanding how to evaluate a specific term in a sequence defined by a formula.
  • Quadratic Functions – Recognizing that the formula involves a quadratic expression and applying basic arithmetic.
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