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

NDA 2022 · Mathematics · Sequences and Series

Paragraph: Let P be the sum of first n positive terms of an...

Paragraph: Let PP be the sum of first nn positive terms of an increasing arithmetic progression AA. Let QQ be the sum of first nn positive terms of another increasing arithmetic progression BB. Let P:Q=(5n+4):(9n+6)P: Q=(5 n+4):(9 n+6)
Question: What is the ratio of their 10th terms?

Options

  1. A1129\frac{11}{29}
  2. B2249\frac{22}{49}
  3. C3359\frac{33}{59}
  4. D4469\frac{44}{69}

Correct answer

C. 3359\frac{33}{59}

Step-by-step solution

SnSn′=5n+49n+6⇒2a+(n−1)d2a′+(n−1)d′=5n+49n+6\begin{aligned} & \frac{S_n}{S_n^{\prime}}=\frac{5 n+4}{9 n+6} \\ & \Rightarrow \frac{2 a+(n-1) d}{2 a^{\prime}+(n-1) d^{\prime}}=\frac{5 n+4}{9 n+6} \end{aligned} Put n=19n=19⇒2a+18d2a′+18d′=95+4171+6⇒a+9da′+9d′=99177⇒a10a101=3359\begin{aligned} & \Rightarrow \frac{2 a+18 d}{2 a^{\prime}+18 d^{\prime}}=\frac{95+4}{171+6} \\ & \Rightarrow \frac{a+9 d}{a^{\prime}+9 d^{\prime}}=\frac{99}{177} \Rightarrow \frac{a_{10}}{a_{10}{ }^1}=\frac{33}{59} \end{aligned}$$
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