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NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Sequences and Series

NDA 2011 · Mathematics · Sequences and Series

If the 10^ th term of a GP is 9 and 4^ th term is 4 , then what is...

If the 10th 10^{\text{th }} term of a GP is 9 and 4th 4^{\text{th }} term is 4 , then what is its 7th 7^{\text{th }} term?

Options

  1. A66
  2. B1414
  3. C27/14
  4. D56/15

Correct answer

A. 66

Step-by-step solution

Let first term of G.P. is aa and common ratio =r∵10th =r\because 10^{\text{th }} term of G.P. is 9 ⇒ar9=9\Rightarrow \quad a r^9=9 ...(i)andar3=4and a r^3=4 (ii) Divide (i) by (ii) ar9ar3=94⇒r6=94⇒(r3)2=(32)2r3=32\frac{a r^9}{a r^3}=\frac{9}{4} \Rightarrow r^6=\frac{9}{4}\Rightarrow \quad\left(r^3\right)^2=\left(\frac{3}{2}\right)^2r^3=\frac{3}{2} Putting the value of r3r^3 in (i) ar3=4a(32)=4⇒a=837th a r^3=4a\left(\frac{3}{2}\right)=4 \quad \Rightarrow a=\frac{8}{3}7^{\text{th }} term =ar6=83×94=6=a r^6=\frac{8}{3} \times \frac{9}{4}=6.
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