Enter a recursive rule for the geometric sequence.
4, −16, 64, −256,
a1=
an=

Step-by-step explanation:

Given a G.P series i.e geometric sequence

4, −16, 64, −256, ...

We have to find the recursive rule for the geometric sequence.

We know that   is the first term of the sequence.

Here

As, the nth term of Geometric progression is

where r is the common ratio

Hence the recursive formula is

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.