What is the 5th term of the sequence defined by a_n = 2n^2 + 3n - 1?

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Question: What is the 5th term of the sequence defined by a_n = 2n^2 + 3n - 1?

Options:

Correct Answer: 47

Solution:

To find the 5th term, substitute n = 5 into the formula: a_5 = 2(5^2) + 3(5) - 1 = 2(25) + 15 - 1 = 50 + 15 - 1 = 64.

What is the 5th term of the sequence defined by a_n = 2n^2 + 3n - 1?

What is the 5th term of the sequence defined by a_n = 2n^2 + 3n - 1?

Step 1: Identify the formula for the sequence, which is a_n = 2n^2 + 3n - 1.
Step 2: Determine which term you need to find. In this case, we need the 5th term, so set n = 5.
Step 3: Substitute n = 5 into the formula: a_5 = 2(5^2) + 3(5) - 1.
Step 4: Calculate 5^2, which is 25.
Step 5: Multiply 25 by 2: 2 * 25 = 50.
Step 6: Calculate 3 * 5, which is 15.
Step 7: Now combine the results: a_5 = 50 + 15 - 1.
Step 8: Add 50 and 15 to get 65.
Step 9: Subtract 1 from 65 to get the final result: 65 - 1 = 64.

Quadratic Sequences – Understanding how to evaluate a quadratic function for specific integer values.
Substitution – The process of substituting a specific value into a formula to find a term in a sequence.