Question Write an explicit formula for \( a_{n} \), the \( n^{\text {th }} \) term of the sequence \( 30,35,40, \ldots \) Answer Attempt 1 out of 3 \( a_{n}=\square \) Submit Answer
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The sequence given is an arithmetic sequence where each term increases by 5. To find the explicit formula for the \( n^{\text{th}} \) term, you can start with the first term \( a_1 = 30 \) and add the common difference multiplied by \( (n-1) \). Therefore, the formula is: \[ a_{n} = 30 + 5(n-1) \] This simplifies to: \[ a_{n} = 5n + 25 \] So, the explicit formula for \( a_{n} \) is \( a_{n} = 5n + 25 \). The beauty of arithmetic sequences like this is that they're easier to work with than you might think! You can find any term without having to list them all out—just plug in the value of \( n \) and voilà! Want the 20th term? Just pop 20 into the formula, and you're all set! Easy peasy!
