Most Important Selected Qs for JEE AdvancedMathematicsSequences and Series
a, b, c are the first three terms of geometric series. If the H.M. of a and b is 12 and that of b and c is 36 then which of the following hold(s) good?
Options
- ASum of the first term and common ratio of the G.P. is 11.
- BSum of the first five terms of the G.P. is 948 .
- CIf the value of the the first term and common ratio of the given G.P. is taken as the first term and common di
- DThe number 648 is one of the term of the G.P.
Correct answer
D. The number 648 is one of the term of the G.P.
Step-by-step solution
a, b, c are in G.P.; b=a r, c=a r^212= 2 a b a+b a b a+b =6 a^2 r a(1+r) =6 a r 1+r =6 .....(1) again 36= 2 b c b+c b c b+c =18 a ^2 r ^3 ar (1+ r ) =18 ar ^2 1+ r =18 .....(2) from (1) and (2), a = 8, r=3 now verify all the alternatives