Find the 10th term of the sequence where a_n = 3n - 1.
Understand the Problem
The question is asking to find the 10th term of a sequence defined by the formula a_n = 3n - 1. This involves substituting n = 10 into the formula to calculate the term.
Answer
The 10th term of the sequence is \( 29 \).
Answer for screen readers
The 10th term of the sequence is ( 29 ).
Steps to Solve
- Substituting n into the formula
To find the 10th term, substitute ( n = 10 ) into the formula ( a_n = 3n - 1 ).
- Performing the calculation
Now, substitute ( n ) in the formula:
$$ a_{10} = 3(10) - 1 $$
- Calculating the value
Carry out the multiplication and subtraction:
$$ a_{10} = 30 - 1 $$
- Final calculation result
Now, subtract to find the final value of ( a_{10} ):
$$ a_{10} = 29 $$
The 10th term of the sequence is ( 29 ).
More Information
The sequence defined by ( a_n = 3n - 1 ) is linear, and the formula allows for quick computation of any term by simply plugging in the value of ( n ).
Tips
- Forgetting to substitute ( n ) correctly in the formula.
- Miscalculating basic arithmetic operations, especially subtraction.
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