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

NDA 2022 · Mathematics · Sequences and Series

If the 5th term of an AP is (1)/(10) and its 10 th term is (1)/(5)...

If the 5th term of an AP is 110\frac{1}{10} and its 10 th term is 15\frac{1}{5}, then what is the sum of first 50 terms?

Options

  1. A25
  2. B25.5
  3. C26
  4. D26.5

Correct answer

B. 25.5

Step-by-step solution

a5=110⇒a+4d=110a_5=\frac{1}{10} \Rightarrow a+4 d=\frac{1}{10}...(i) ⇒a10=15⇒a+9d=15\Rightarrow \quad \mathrm{a}_{10}=\frac{1}{5} \Rightarrow \mathrm{a}+9 \mathrm{ d}=\frac{1}{5}...(ii) from (i) and (ii), we get a=150\mathrm{a}=\frac{1}{50} and d=150∴S50=502[250+4950]=502×5150=25.5\mathrm{d}=\frac{1}{50}\therefore \mathrm{S}_{50}=\frac{50}{2}\left[\frac{2}{50}+\frac{49}{50}\right]=\frac{50}{2} \times \frac{51}{50}=25.5
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