Question

find x
if 2x+1, x²+x+1 and 3x² - 3x + 3
consecutive term of
AP.
​

Answer 1

Answer:

x= -1,2/5

Step-by-step explanation:

Using AP,

You can use any method of your choice...

Hope it helps

:)

Answer 2

Answer :

x = 1 (or) 2

Step-by-step explanation :

  $\underline{\underline{\bf Arithmetic \ Progression :}}$

•     It is the sequence of numbers such that the difference between any two successive numbers is constant.

•      In AP,

        a - first term

        d - common difference

        aₙ - nth term

        Sₙ - sum of n terms

•   General form of AP,

           a , a+d , a+2d , a+3d , ..........

•    Formulae :-

            nth term of AP,

           $\boxed{\bf a_n=a+(n-1)d}$

          Sum of n terms in AP,

          $\boxed{\bf S_n=\frac{n}{2}[2a+(n-1)d]}$

____________________________

Given,

2x+1, x²+x+1 and 3x² - 3x + 3 are the consecutive terms of AP.

In AP, difference of any two consecutive terms is constant.

                 

             x² + x + 1 - (2x + 1) = 3x² - 3x + 3 - (x² + x + 1)

             x² + x + 1 - 2x - 1 = 3x² - 3x + 3 - x² - x - 1

              x² - x = 2x² - 4x + 2

              2x² - x² = 4x - x - 2

                x² = 3x - 2

               x² - 3x + 2 = 0

              x² - x - 2x + 2 = 0

             x(x - 1) - 2(x - 1) = 0

             (x - 1) (x - 2) = 0

=> x = 1 (or) 2

• If x = 1,

      the terms are 3,3,3

• If x = 2,

      the terms are 5,7,9