The sum of the $3^{r d}$ and the $4^{t h}$ terms of a G.P. is 60 and the product of its first three terms is 1000. If the first term of this G.P. is positive, then its $7^{t h}$ term is

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

640

7290

320

2430

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$a r^{2} + a r^{3} = 60 and a \times a r \times a r^{2} = 1000$

$\begin{array}{l} \Rightarrow a r (r + r^{2}) = 60 and a^{3} r^{3} = 1000 \Rightarrow a r = 10 \\ \Rightarrow r + r^{2} = 6 \Rightarrow r = - 3, 2 \\ \Rightarrow r = 2 \Rightarrow a = 5 \\ ∴ T_{7} = a r^{6} = 5 \times 2^{6} = 320 \end{array}$

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!