If the first term of a G.P. a1, a2, a3 .... is unity  such that 4a2 + 5a3 is least then the common ratio of G.P. is  a) -2/5   b)  -3/5  c)  2/5  d) none of these

Asked by ahuja8087 | 13th Nov, 2015, 02:12: PM

Expert Answer:

G i v e n space t h a t space a subscript 1 comma space a subscript 2 comma space a subscript 3 comma... comma a subscript n space a r e space t e r m s space o f space a space G P. A l s o space g i v e n space t h a t space a subscript 1 equals 1 T h u s comma space t h e space t e r m s space a r e space 1 comma space r comma space r squared comma space r cubed comma space.... space a r e space t h e space t e r m s space o f space t h e space G P. C o n s i d e r space t h e space g i v e n space e x p r e s s i o n comma space 4 a subscript 2 plus 5 a subscript 3 equals 4 r plus 5 r squared L e t space y equals 4 r plus 5 r squared G i v e n space t h a t space y space s h o u l d space b e space m i n i m u m. D i f f e r e n t i a t i n g space t h e space a b o v e space f u n c t i o n space w i t h space r e s p e c t space t o space apostrophe r apostrophe comma space w e space h a v e comma fraction numerator d y over denominator d r end fraction equals 4 plus 10 r S i n c e space i t space i s space m i n i m u m comma space w e space h a v e comma space fraction numerator d y over denominator d r end fraction equals 0 comma rightwards double arrow 4 plus 10 r space equals 0 rightwards double arrow 10 r equals negative 4 rightwards double arrow r equals fraction numerator negative 4 over denominator 10 end fraction space rightwards double arrow r equals fraction numerator negative 2 over denominator 5 end fraction H e n c e space t h e space c o r r e c t space o p t i o n space i s space left parenthesis a right parenthesis.

Answered by Vimala Ramamurthy | 13th Nov, 2015, 06:54: PM