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Find the 10th term of the sequence defined by a_n = 3n^2 + 2n.

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Question: Find the 10th term of the sequence defined by a_n = 3n^2 + 2n.

Options:

  1. 320
  2. 302
  3. 290
  4. 310

Correct Answer: 302

Solution: 

a_10 = 3(10^2) + 2(10) = 300 + 20 = 320.

Find the 10th term of the sequence defined by a_n = 3n^2 + 2n.

Practice Questions

Q1
Find the 10th term of the sequence defined by a_n = 3n^2 + 2n.
  1. 320
  2. 302
  3. 290
  4. 310

Questions & Step-by-Step Solutions

Find the 10th term of the sequence defined by a_n = 3n^2 + 2n.
  • Step 1: Identify the formula for the sequence, which is a_n = 3n^2 + 2n.
  • Step 2: Substitute n with 10 in the formula to find the 10th term: a_10 = 3(10^2) + 2(10).
  • Step 3: Calculate 10^2, which is 100.
  • Step 4: Multiply 3 by 100 to get 300.
  • Step 5: Calculate 2 times 10, which is 20.
  • Step 6: Add the results from Step 4 and Step 5: 300 + 20.
  • Step 7: The final result is 320, which is the 10th term of the sequence.
  • Quadratic Sequences – The question tests the understanding of how to evaluate a quadratic function at a specific integer value.
  • Substitution – The question requires substituting a specific value (n=10) into the given formula.
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