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(IS) fint a=2200 secquad2250 flued =+230 200,250,300,350 dots {:[a=2a quad d=50],[n=30quad5n],[S_(n)=(n)/(2)(2a+(n-1","d)]:}

(IS)\newlinefint a=2200 a=2200 \newlinesec2250 \mathrm{sec} \quad 2250 \newlineflued =+230 =+230 \newline200,250,300,350… 200,250,300,350 \ldots \newlineaamp;=2ad=50namp;=305nSnamp;=n2(2a+(n−1,d) \begin{aligned} a & =2 a \quad d=50 \\ n & =30 \quad 5 n \\ S_{n} & =\frac{n}{2}(2 a+(n-1, d) \end{aligned} \newlineA) 200200\newlineB) 250250\newlineC) 300300\newlineD) 350350

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Q. (IS)\newlinefint a=2200 a=2200 \newlinesec2250 \mathrm{sec} \quad 2250 \newlineflued =+230 =+230 \newline200,250,300,350… 200,250,300,350 \ldots \newlinea=2ad=50n=305nSn=n2(2a+(n−1,d) \begin{aligned} a & =2 a \quad d=50 \\ n & =30 \quad 5 n \\ S_{n} & =\frac{n}{2}(2 a+(n-1, d) \end{aligned} \newlineA) 200200\newlineB) 250250\newlineC) 300300\newlineD) 350350
  1. Identify Terms: Identify the first term aa and common difference dd. a=2200a = 2200 d=50d = 50
  2. Identify Number: Identify the number of terms (\newline). n=30n = 30
  3. Use Sum Formula: Use the sum formula for an arithmetic sequence: Sn=n2(2a+(n−1)d) S_n = \frac{n}{2} (2a + (n-1)d) .
  4. Substitute Values: Substitute the values into the formula.\newlineS30=302(2⋅2200+(30−1)⋅50) S_{30} = \frac{30}{2} (2 \cdot 2200 + (30-1) \cdot 50)
  5. Simplify Calculation: Simplify inside the parentheses.\newlineS30=15(4400+29⋅50) S_{30} = 15 (4400 + 29 \cdot 50)
  6. Calculate Product: Calculate 29⋅50 29 \cdot 50 .\newline29⋅50=1450 29 \cdot 50 = 1450
  7. Add Results: Add the results inside the parentheses.\newline4400+1450=5850 4400 + 1450 = 5850
  8. Multiply by 1515: Multiply by 1515.\newlineS30=15⋅5850 S_{30} = 15 \cdot 5850
  9. Calculate Final Sum: Calculate the final sum.\newline15⋅5850=87750 15 \cdot 5850 = 87750

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