Which table represents an arithmethic sequence?

Table 3  represents an arithmetic sequence.

Solution:

To find which table represents an arithmetic sequence:

In arithmetic sequence difference of each term is equal.

Table 1:

  = –12 – (–6)

d = –6

  = –24 – (–12)

d = –12

Here differences are not equal.

So table 1 not represents an arithmetic sequence.

Table 2:

  = 9 – 7

d = 2

  = 13 – 9

d = 4

Here differences are not equal.

So table 2 not represents an arithmetic sequence.

Table 3:

  = 7.3 – 8.7

d = –1.4

  = 5.9 – 7.3

d = –1.4

  = 4.5 – 5.9

d = –1.4

  = 3.1 – 4.5

d = –1.4

Here differences are equal.

So table 3 represents an arithmetic sequence.

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.

answer: you need to organize this better it does not make sense.

step-by-step explanation: ?