\( S_9 = 3(81) + 5(9) = 243 + 45 = 288 \)
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- The sum of the first \( n \) terms of an arithmetic sequence is \( S_n = 3n^2 + 5n \). Find the 10th term.
- The \( n \)-th term is \( a_n = S_n - S_{n-1} \).
- \( S_{10} = 3(100) + 5(10) = 300 + 50 = 350 \)
- \( a_{10} = 350 - 288 = 62 \)
- #### 10th term: 62
- A ball is thrown upward from a 45-meter tall building with initial velocity 20 m/s. Its height is modeled by \( h(t) = -5t^2 + 20t + 45 \). When does it hit the ground?
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