Find an explicit formula for the arithmetic sequence 170,85,0,-85...,
d(n)=

d(n) = 85 * ( 3 - n )

Step-by-step explanation:

Let's find the common difference of the terms (if any).

The common difference is = 85 - 170 = 0 - 85 = -85 - 0 = -85

For an arithmatic sequence with first term a, common difference d,

  nth term = a + ( n - 1 ) * d

So, d(n) = 170 + ( n - 1 ) * (-85)

             = 255 - 85n

             = 85 ( 3 - n )

[ If there's any mistake, please inform me ]

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.