Question

If -5/7, a, 2 are consecutive terms in an Arithmetic Progression, Find the value of a.

Answer 1

Answer :

a = 9/14

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,

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

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Given,

-5/7, a, 2 are consecutive terms in an Arithmetic Progression

we know,

The difference between any two consecutive terms in AP is constant.

         

           $\longrightarrow \ \ a -(\frac{-5}{7} )=2-a \\\\ \longrightarrow \ \ a+\frac{5}{7} =2-a \\\\ \longrightarrow \ \ a+a=2-\frac{5}{7} \\\\ \longrightarrow \ \ 2a=\frac{14-5}{7} \\\\ \longrightarrow \ \ 2a=\frac{9}{7} \\\\ \longrightarrow \ \ a=\frac{9}{7 \times 2} \\\\ \longrightarrow \ \ a=\frac{9}{14}$

║ The value of a is 9/14.