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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Sequences and Series

NDA 2022 · Mathematics · Sequences and Series

If the sum of the first 9 terms of an AP is equal to sum of the...

If the sum of the first 9 terms of an AP is equal to sum of the first 11 terms, then what is the sum of the first 20 terms?

Options

  1. A20
  2. B10
  3. C2
  4. D0

Correct answer

D. 0

Step-by-step solution

According to questionsquestionsS9=S1192(2a+8d)=112(2a+10d)⇒18a+72d=22a+110d⇒4a+38d=0⇒2a+19d=0∴S20=202(2a+19d)=0\begin{aligned} & \mathrm{S}_9=\mathrm{S}_{11} \\ & \frac{9}{2}(2 \mathrm{a}+8 \mathrm{ d})=\frac{11}{2}(2 \mathrm{a}+10 \mathrm{ d}) \\ & \Rightarrow 18 \mathrm{a}+72 \mathrm{ d}=22 \mathrm{a}+110 \mathrm{ d} \\ & \Rightarrow 4 \mathrm{a}+38 \mathrm{ d}=0 \Rightarrow 2 \mathrm{a}+19 \mathrm{ d}=0 \\ & \therefore \mathrm{ S}_{20}=\frac{20}{2}(2 \mathrm{a}+19 \mathrm{ d})=0\end{aligned}$$
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