NDA2020MathematicsSequences and SeriesActual
If p^2, q^2 and r^2 (where .p, q, r 0 ) are in GP, then which of the following is/are correct? 1. p, q and r are in GP. 2. p, q and r are in AP . Select the correct answer using the code given below :
Options
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Correct answer
C. Both 1 and 2
Step-by-step solution
(1) p^2, q^2 and r^2 in G.P. Then, (q^2 )^2=p^2 r^2 q^2= (p^2 r^2 )^ 1 2 q^2=p r Hence, p, q and r in G.P. (2) As, q^2=p r Taking on both sides, we have aligned & (q^2 )= (p r) & 2 (q)= p+ r aligned Hence, p, q and r are in A.P.