(i)Which term of the A.P. `4, 3(5)/(7), 3(3)/(7), .....` is the first negative term?
(ii) Which term of the progression `20, 19(1)/(2), 18(1)/(2), 17(3)/(4),....` is the first negative term?
Correct Answer - D
`(d)` Let the `4` roots be `x-3y`, `x-y`, `x+y`, `x+3y`
`"sum"=4x` and if `4x=0` then `4` roots are `-3y`, `-y`, `y`,`3y` and the product is `9y^(4)=225impliesy^(2)=5`.
The...
Correct Answer - C
`(c )` `(a_(100)+b_(100))-(a_(1)+b_(1))=99dimpliesd=0`
`:.` Sum of series `=(100//2)(a_(100)+b_(100)+a_(1)+b_(1))`
`=50(100+100)`
`=10000`
let the 4 terms be a - 3d, a-d, a+d and a+3d
Sum = 4a = 36, so a = 9
Product of 2nd and 4th = (9-d)(9+3d)=105
81+27d-9d-3d2 = 105
3d2-18d+24=0
d2-6d+8=0
(d-2)(d-4)=0
so d=2, or...
