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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Sequences and Series

NDA 2018 · Mathematics · Sequences and Series

The third term of a GP is 3. What is the product of the first five...

The third term of a GP is 3. What is the product of the first five terms?

Options

  1. A216
  2. B226
  3. C243
  4. DCannot be determined due to insufficient data

Correct answer

C. 243

Step-by-step solution

Given, 3rd 3^{\text{rd }} term of G.P. =3=3 Let ' aa ' be the first term and ' rr ' be the common ratio. ∴ar2=3\therefore \mathrm{ar}^2=3 We know, T1=a,T2=ar,T3=ar2,T4=ar3,T5=ar4\mathrm{T}_1=\mathrm{a}, \mathrm{T}_2=\mathrm{ar}, \mathrm{T}_3=\mathrm{ar}^2, \mathrm{ T}_4=\mathrm{ar}^3, \mathrm{ T}_5=\mathrm{ar}^4T1⋅T2⋅T3⋅T4⋅T5=(a)(ar)(ar2)(ar3)(ar4)=a5r10=(ar2)5=35=243\begin{aligned} & \mathrm{T}_1 \cdot \mathrm{ T}_2 \cdot \mathrm{ T}_3 \cdot \mathrm{ T}_4 \cdot \mathrm{ T}_5=(\mathrm{a})(\mathrm{ar})\left(\mathrm{ar}^2\right)\left(\mathrm{ar}^3\right)\left(\mathrm{ar}^4\right) \\ & =\mathrm{a}^5 \mathrm{r}^{10}=\left(\mathrm{ar}^2\right)^5=3^5=243 \end{aligned}$$
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