Please answer this ASAP

Here's the solution ~

The first term (a) of the sequence is 1

common difference (d) = -2 - (1) = -3

last term (l) is -236, so let's find the number of terms in the given progression ~

So, there are total of 80 terms in the sequence.

now, as we know ! in a Arithmetic progression the sum of all the terms is :

Now, let's use this formula ~

or we can use method ll where, the first and last terms are given ~

let's use similar procedure :

Now, let's find the sum ~

[ I'm taking first term as a1 ]

Let's use the formula ~

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

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.