\( S_{10} = \frac{10}{2}(2 \times 5 + (10-1) \times 3) \)
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- \( a_4 = 3 \times 34 + 4 = 106 \)
- #### 106
- The sum of the first \( n \) terms of an arithmetic series is given by \( S_n = \frac{n}{2}(2a + (n-1)d) \). If the first term \( a = 5 \) and the common difference \( d = 3 \), what is the sum of the first 10 terms?
- \( S_{10} = 5(10 + 27) = 5 \times 37 = 185 \)
- Solve for \( x \) in the equation \( 2x^2 - 3x - 5 = 0 \) using the quadratic formula.
- Here, \( a = 2 \), \( b = -3 \), \( c = -5 \).
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