Let $$p$$ and $$q$$ be roots of the equation $${x^2} - 2x + A = 0$$ and let $$r$$ and $$s$$ be the roots of the equation $${x^2} - 18x + B = 0.$$ If $$p < q < r < s$$ are in arithmetic progression, then $$A = \,..........$$ and $$B = \,..........$$
Let the harmonic mean and geometric mean of two positive numbers be the ratio 4 : 5. Then the two number are in the ratio .........
Answer
4 : 1 or 1 : 4
4
IIT-JEE 1988
Fill in the Blanks
The sum of the first n terms of the series $${1^2} + {2.2^2} + {3^2} + {2.4^2} + {5^2} + {2.6^2} + .........$$ is
$$n\,\,{\left( {n + 1} \right)^2}/2,$$ when $$n$$ is even. When $$n$$ is odd, the sum is .............
Answer
$${{{n^2}\left( {n + 1} \right)} \over 2}$$
Questions Asked from Sequences and Series
On those following papers in Fill in the Blanks
Number in Brackets after Paper Indicates No. of Questions